BITSAT 2024 | Circle Question 1 | Mathematics

The locus of the point of intersection of the lines $ x=a\left(\frac{1-t^{2}}{1+t^{2}}\right) $ and $ y=\frac{2 a t}{1+t^{2}} $ represent $ (t $ being a parameter)

Circle

Parabola

Ellipse

Hyperbola

BITSAT 2024

MCQ (Single Correct Answer)

-1

The locus of the mid-point of a chord of the circle $ x^{2}+y^{2}=4 $, which subtends a right angle at the origin is

$ x+y=2 $

$ x^{2}+y^{2}=1 $

$ x^{2}+y^{2}=2 $

$ x+y=1 $

BITSAT 2023

MCQ (Single Correct Answer)

-1

If the straight line $$y=m x+c$$, touches the circle $$x^2+y^2=a^2$$ at a point, then $$c^2$$ is

$$m^2\left(1-a^2\right)$$

$$m^2\left(1+a^2\right)$$

$$a^2\left(1-m^2\right)$$

$$a^2\left(1+m^2\right)$$

BITSAT 2023

MCQ (Single Correct Answer)

-1

A normal is drawn at the point $$P$$ to the circle $$x^2+y^2=25$$, which is inclined at $$45^{\circ}$$ with the straight line $$y=6$$. Then, the point lies on the straight line

$$y=x$$

$$y=-x$$

$$y=\sqrt{3} x$$

$$\sqrt{3} y=x$$

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