Circle · Mathematics · MHT CET

Two tangents to the circle $x^2+y^2=4$ at the points A and B meet at $\mathrm{P}(-4,0)$. Then the area of quadrilateral PAOB, where ' $O$ ' is the origin is

The least distance of the point $\mathrm{A}(10,7)$ from the circle $x^2+y^2-4 x-2 y-20=0$ is length of seg AM . If $\mathrm{MM}^{\prime}$ is the diameter of the circle, then the lengths of AM and $\mathrm{AM}^{\prime}$ are respectively ___________ , ____________units

If a circle with centre at $(-1,1)$ touches the line $x+2 y+4=0$ then the co-ordinates of the point of contact are

A pair of tangents are drawn to the circle $x^2+y^2+6 x-4 y-12=0$ from a point $\mathrm{P}(-4,-5)$, then the area enclosed between these tangents and the area of the circle is

The equations of the tangents to the circle $x^2+y^2=36$ which are perpendicular to the line $5 x+y-2=0$ are

Let the circle with centre at origin pass through the vertices of an equilateral triangle ABC . If $A \equiv(2,4)$, then the length of the median through A is

The equations of the tangents to the circle $x^2+y^2=36$ which are perpendicular to the line $5 x+y=2$, are

If the tangent and the normal at the point $(\sqrt{3}, 1)$ to the circle $x^2+y^{2 }=4$, and the X -axis form a triangle, then the area (in sq.units) of this triangle is

The locus of point of intersection of the tangents to the circle $x^2+y^2=16$, such that the angle between them is $60^{\circ}$, is

The minimum distance and maximum distance of the point $\mathrm{P}(2,-7)$ from the circle $x^2+y^2-14 x-10 y-151=0$ are respectively _______units

The number of integral values of $k$ for which $x^2+y^2+\mathrm{k} x+(1-\mathrm{k}) y+5=0$ represents a circle whose radius cannot exceeds 5 , are

The equation of the circle passing through the point $(1,1)$ and having two diameters along the pair of lines $x^2-y^2-2 x+4 y-3=0$ is

If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16 x+12 y+\mathrm{C}=0$, then $\mathrm{C}=$

One end of the diameter of the circle $x^2+y^2-6 x-5 y-1=0$ is $(-1,3)$, then the equation of the tangent at the other end of the diameter is

The equation of the circle, concentric with the circle $2 x^2+2 y^2-6 x+8 y+1=0$ and double of its area is

If the sides of a rectangle are given by the equations $x=-2, x=6, y=-2, y=5$, then the equation of the circle, drawn on the diagonal of this rectangle as its diameter, is

The number of common tangents to the circles $x^2+y^2-x=0$ and $x^2+y^2+x=0$ is /are

The parametric equations of the circle $x^2+y^2-\mathrm{a} x-b y=0$ are

The equation of the tangent to the circle, given by $x=5 \cos \theta, y=5 \sin \theta$ at the point $\theta=\frac{\pi}{3}$ on it , is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius $r$. If PS and RQ intersect at a point X on the circumference of the circle, then 2 r equals

The abscissae of the two points A and B are the roots of the equation $x^2+2 a x-b^2=0$ and their ordinates are roots of the equation $y^2+2 p y-q^2=0$. Then the equation of the circle with AB as diameter is given by

The equation of the circle, concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the $\mathrm{X}$-axis is

The equation of the circle, the end points of whose diameter are the centres of the circles $x^2+y^2+6 x-14 y+5=0$ and $x^2+y^2-4 x+10 y-4=0$ is

The equation of the circle which passes through the centre of the circle $x^2+y^2+8 x+10 y-7=0$ and concentric which the circle $2 x^2+2 y^2-8 x-12 y-9=0$ is

The equation of the circle which has its centre at the point $(3,4)$ and touches the line $5 x+12 y-11=0$ is

The tangent to the circle $x^2+y^2=5$ at $(1,-2)$ also touches the circle $x^2+y^2-8 x+6 y+20=0$ then the co-ordinates of the corresponding point of contact is

The equation of the concentric circle, with the circle $\mathrm{C}_1$ having equation $x^2+y^2-6 x-4 y-12=0$ and having double area compared to the area of $\mathrm{C}_1$, is

Two tangents drawn from $\mathrm{P}(1,7)$ to the circle $x^2+y^2=25$, touch the circle at Q and R respectively. The area of the quadrilateral PQOR is

If $\left(m_i, \frac{1}{m_i}\right), m_i>0, i=1,2,3,4$ are four distinct points on a circle, then the product $\mathrm{m}_1 \mathrm{~m}_2 \mathrm{~m}_3 \mathrm{~m}_4$ is equal to

The centre of the circle whose radius is 3 units and touching internally the circle $$x^2+y^2-4 x-6 y-12=0$$ at the point $$(-1,-1)$$ is

If the line $$x-2 y=\mathrm{m}(\mathrm{m} \in \mathrm{Z})$$ intersects the circle $$x^2+y^2=2 x+4 y$$ at two distinct points, then the number of possible values of $m$ are

The abscissae of two points $$A$$ and $$B$$ are the roots of the equation $$x^2+2 a x-b^2=0$$ and their ordinates are roots of the equation $$y^2+2 p y-q^2=0$$. Then, the equation of the circle with $$A B$$ as diameter is given by

The parametric equations of the curve $$x^2+y^2+a x+b y=0$$ are

The circles $$x^2+y^2+2 \mathrm{a} x+\mathrm{c}=0$$ and $$x^2+y^2+2 b y+c=0$$ touch each other externally, if

If $$\lambda$$ is the perpendicular distance of a point $$\mathrm{P}$$ on the circle $$x^2+y^2+2 x+2 y-3=0$$, from the line $$2 x+y+13=0$$, then maximum possible value of $$\lambda$$ is

If a circle passes through points $$(4,0)$$ and $$(0,2)$$ and its centre lies on $$\mathrm{Y}$$-axis. If the radius of the circle is $$r$$, then the value of $$r^2-r+1$$ is

Number of common tangents to the circles $$x^2+y^2-6 x-14 y+48=0$$ and $$x^2+y^2-6 x=0$$ are

The parametric equations of the circle $$x^2+y^2+2 x-4 y-4=0$$ are

If the circles $$x^2+y^2=9$$ and $$x^2+y^2+2 \alpha x+2 y+1=0$$ touch each other internally, then the value of $$\alpha^3$$ is

The sides of a rectangle are given by the equations $$x=-2, x=4, y=-2$$ and $$y=5$$

Then the equation of the circle, whose centre is the point of intersection of the diagonals, lying within the rectangle and touching only two opposite sides, is

Two tangents to the circle $$x^2+y^2=4$$ at the points $$\mathrm{A}$$ and $$\mathrm{B}$$ meet at the point $$\mathrm{P}(-4,0)$$. Then the area of the quadrilateral $$\mathrm{PAOB}, \mathrm{O}$$ being the origin, is

If the lines $$3 x-4 y-7=0$$ and $$2 x-3 y-5=0$$ pass through diameters of a circle of area $$49 \pi$$ square units, then the equation of the circle is

If $$y=2 x$$ is a chord of circle $$x^2+y^2-10 x=0$$, then the equation of circle with this chord as diameter is

Equationof the chord of the circle $$x^2+y^2-4 x-10 y+25=0$$ having mid-point $$(1,2)$$ is

The equation of common tangent to the circles $$x^2+y^2-4 x+10 y+20=0$$ and $$x^2+y^2+8 x-6 y-24=0$$ is

If a circle passes through the points $$(0,0),(x, 0)$$ and $$(0, y)$$, then the coordinates of its centre are

Two circles centred at $$(2,3)$$ and $$(4,5)$$ intersects each other. If their radii are equal, then the equation of the common chord is

The equation of a circle that passes through the origin and cut off intercepts $$-2$$ and 3 on the $$\mathrm{X}$$-axis and $$\mathrm{Y}$$-axis respectively is

The equation of circle with centre at $$(2,-3)$$ and the circumference $$10 \pi$$ units is

The equation of the circle whose centre lies on the line $$x-4 y=1$$ and which passes through the points $$(3,7)$$ and $$(5,5)$$ is

If the lines $$3x - 4y + 4 = 0$$ and $$6x - 8y - 7 = 0$$ are tangents to a circle, then the radius of the circle is

The radius of the circle passing through the points $$(5,7),(2,-2)$$ and $$(-2,0)$$ is

The intercept on the line $y=x$ by the circle $x^2+y^2-2 x=0$ is $A B$. The equation of the circle with $A B$ as a diameter is .............

The equation of the circle concentric with the circle $x^2+y^2-6 x-4 y-12=0$ and touching the $Y$-axis is ............

The general solution of the differential equation of all circles having centre at $A(-1,2)$ is ........