BITSAT 2025 | Circle Question 2 | Mathematics

What is the set of values of a for which the point ( $2 a, a+1$ ) is an interior point of the larger segment of the circle $x^2+y^2-2 x-2 y-8=0$ made by the chord $x-y+1=0$.

$\left(0, \frac{9}{5}\right)$

$(0, \infty)$

$\left(\frac{9}{5}, \infty\right)$

$(-\infty, 0)$

BITSAT 2024

MCQ (Single Correct Answer)

-1

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

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

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

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

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

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