TS EAMCET 2023 (Online) 12th May Evening Shift | Parabola Question 11 | Mathematics

The normal at a point on the parabola $y^2=4 x$ passes through $(5,0)$. If there are two more normals to this parabola passing through $(5,0)$, then the equation of one of these normals is

$2 x-y-10=0$

$x+y-5=0$

$\sqrt{3} x+2 y+5 \sqrt{3}=0$

$\sqrt{3} x-y-5 \sqrt{3}=0$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

The equations of common tangents to the parabola $y^2=16 x$ and the circle $x^2+y^2=8$ are

$y=x+2, y=x-2$

$y=x+1, y=x-2$

$y=2 x+4, y=-2 x+4$

$y=x+4, y=-x-4$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

If two circles $x^2+y^2-6 x-6 y+13=0$ and $x^2+y^2-8 y+9=0$ intersect at $A$ and $B$, then the focus of the parabola whose directrix is the line $A B$ and vertex is the point $s(a, b)$ is

$\left(\frac{3}{5}, \frac{1}{5}\right)$

$\left(-\frac{3}{5}, \frac{1}{5}\right)$

$\left(-\frac{3}{5},-\frac{1}{5}\right)$

$\left(\frac{3}{5},-\frac{1}{5}\right)$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

Two tangents are drawn from the point $(-1,-2)$ to the parabola $y^2=4 x$. If $\theta$ is the angle between these tangents, then $\tan \theta=$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{6}$

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