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1
TG EAPCET 2024 (Online) 9th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$L_1^{\prime}$ is the end of a latus rectum of the ellipse $3x=2 \pm \frac{\sqrt{5}}{\sqrt{5}}$ $3 x^2+4 y^2=12$ which is lying in the third quadrant. If the normal drawn at $L_1^{\prime}$ to this ellipse intersects the ellipse again at the point $P(a, b)$, then $a=$
A
$\frac{63}{38}$
B
$\frac{11}{19}$
C
$-\frac{11}{19}$
D
$-\frac{63}{38}$
2
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $6 x-5 y-20=0$ is a normal to the ellipse $x^2+3 y^2=K$, then $K=$
A
9
B
17
C
25
D
37
3
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The locus of the mid-points of the intercepted portion of the tangents by the coordinate axes, which are drawn to the ellipse $x^2+2 y^2=2$ is

A
$\frac{1}{2 x^2}+\frac{1}{4 y^2}=1$
B
$\frac{1}{4 x^2}+\frac{1}{2 y^2}=1$
C
$\frac{x^2}{2}+\frac{y^2}{4}=1$
D
$\frac{x^2}{4}+\frac{y^2}{2}=1$
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The product of the lengths of the perpendiculars drawn from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ to the tangent at any point on the ellipse is

A
6
B
7
C
8
D
9
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