AP EAPCET 2024 - 20th May Morning Shift | Circle Question 8 | Mathematics

If the line segment joining the points $(1,0)$ and $(0,1)$ subtends an angle of $45^{\circ}$ at a variable point $P$, then the equation of the locus of $P$ is

$\left(x^2+y^2-1\right)\left(x^2+y^2-2 x-2 y+1\right)=0, x \neq 0,1$

$\left(x^2+y^2-1\right)\left(x^2+y^2+2 x+2 y+1\right)=0, x \neq 0,1$

$x^2+y^2+2 x+2 y+1=0$

$x^2+y^2=4$

AP EAPCET 2024 - 20th May Morning Shift

MCQ (Single Correct Answer)

-0

Equation of the circle having its centre on the line $2 x+y+3=0$ and having the lines $3 x+4 y-18=0,3 x+4 y+2=0$ as tangents is

$x^2+y^2+6 x+8 y+4=0$

$x^2+y^2-6 x-8 y+18=0$

$x^2+y^2-8 x+10 y+37=0$

$x^2+y^2+8 x-10 y+37=0$

AP EAPCET 2024 - 20th May Morning Shift

MCQ (Single Correct Answer)

-0

If power of a point $(4,2)$ with respect to the circle $x^2+y^2-2 \alpha x+6 y+\alpha^2-16=0$ is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is

$16+4 \sqrt{6}$

$16+4 \sqrt{6}-6 \sqrt{2}$

$16+4 \sqrt{6}+6 \sqrt{2}$

$16+6 \sqrt{2}$

AP EAPCET 2024 - 20th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $\alpha$ be an integer multiple of 8 . If $S$ is the set of all possible values of $\alpha$ such that the line $6 x+8 y+\alpha=0$ intersects the circle $x^2+y^2-4 x-6 y+9=0$ at two distinct points, then the number of elements in $S$ is

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