## MCQ (Single Correct Answer)

One possible condition for the three points (a, b), (b, a) and (a2, $$-$$ b2) to be collinear is

The distance between the lines $$5x - 12y + 65 = 0$$ and $$5x - 12y - 39 = 0$$ is

The co-ordinates of the foot of perpendicular from (a, 0) on the line $$y = mx + {a \over m}$$ are

If C is a point on the line segment joining A($$-$$3, 4) and B(2, 1) such that AC = 2BC, then the coordinate of C is

The coordinates of the foot of the perpendicular from (0, 0) upon the line x + y = 2 are

A line through the point A(2, 0) which makes an angle of 30$$^\circ$$ with the positive direction of x-axis is rotated about A in clockwise direction ...

If C is the reflection of A(2, 4) in x-axis and B is the reflection of C in y-axis, then $$|AB|$$ is

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is

The point ($$-$$4, 5) is the vertex of a square and one of its diagonals is 7x $$-$$ y + 8 = 0. The equation of the other diagonal is

The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio

If the sum of distances from a point P on two mutually perpendicular straight lines is 1 unit, then the locus of P is a/an

If the three points (3q, 0) (0, 3p) and (1, 1) are collinear then which one is true?

The equations $$y = \pm \sqrt {3x} $$, y = 1 are the sides of

The equations of the lines through (1, 1) and making angles of 45$$^\circ$$ with the line x + y = 0 are

The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are

If the three points A(1, 6), B(3, $$-$$4) and C(x, y) are collinear then the equation satisfying by x and y is

The equation of the locus of the point of intersection of the straight lines $$x\sin \theta + (1 - \cos \theta )y = a\sin \theta $$ and $$x\sin \thet...

A, B are fixed points with coordinates (0, a) and (0, b) (a > 0, b > 0). P is variable point (x, 0) referred to rectangular axis. If the angle $$\angl...

The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents

If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at

The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x - 22y + 1 = 0$$ passes through...

If the algebraic sum of the distances from the points (2, 0), (0, 2) and (1, 1) to a variable straight line be zero, then the line passes through the ...

If the sum of the distances of a point from two perpendicular lines in a plane is 1 unit, then its locus is

If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos$$\theta$$, b sin$$\theta$$) and B(a cos$$\theta$$...

Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular bisector of AB meets the Y-ax...

A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the triangle with vertices (0, 0)...

A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X-axis, the equation of the reflected ray is

The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents

Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the origin. If they have a common lin...

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. The point O divides the segment ...

A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P(a, 0) and ...

A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (...

A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If it intersects the X-axis, the...

A variable line passes through the fixed point $$(\alpha ,\beta )$$. The locus of the foot of the perpendicular from the origin on the line is

If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by $$-$$ d = 0 lies in the 4th quadrant and is equidistant from the two axes, w...

The point Q is the image of the point P(1, 5) about the line y = x and R is the image of the point Q about the line y = $$-$$ X. The circumcentre of t...

The angular points of a triangle are A($$-$$ 1, $$-$$ 7), B(5, 1) and C(1, 4). The equation of the bisector of the angle $$\angle $$ABC is

A line cuts the X-axis at A(5, 0) and the Y-axis at B(0, $$-$$3). A variable line PQ is drawn perpendicular to AB cutting the X-axis at P and the Y-ax...

Transforming to parallel axes through a point (p, q), the equation $$2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0$$ becomes $$2{x^2} + 3xy + 4{y^2} = 1$$....

Let A(2, $$-$$3) and B($$-$$ 2, 1) be two angular points of $$\Delta$$ABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the loc...

The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-$$ x to get the image point Q'...

Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines 3x + 4y = 5 and 12x + 5y = 7, ...

## Subjective

If 2a $$-$$ 5b $$-$$ 3c = 0, show that the straight line ax + by + c = 0 always passes through a fixed point. Find the equation of one straight line p...

The equations to the pairs of opposite sides of a parallelogram are x2 $$-$$ 5x + 6 = 0 and y2 $$-$$ 6y + 5 = 0. Find the equations of its diagonals....

Find the image of the point ($$-$$8, 12) with respect to the line 4x + 7y + 13 = 0.

## MCQ (More than One Correct Answer)

A rectangle ABCD has its side parallel to the line y = 2x and vertices A, B, D are on lines y = 1, x = 1 and x = $$-$$1 respectively. The coordinate o...

Consider the equation $$y - {y_1} = m(x - {x_1})$$. If m and x1 are fixed and different lines are drawn for different values of y1, then...

The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is $$ - 1$$ is

Straight lines x $$-$$ y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB = AC. The equation of line AC...

The area of the triangle formed by the intersection of a line parallel to X-axis and passing through P(h, k), with the lines y = x and x + y = 2 is h2...