1
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

    Consider the parabola $25\left[(x-2)^2+(y+5)^2\right]=(3 x+4 y-1)^2$, match the characteristic of this parabola given in List I with its corresponding item in List II.

    $$ \begin{array}{lll} \hline & \text { List I } & \text { List II } \\\\ \hline \text { I } & \text { Vertex } & \text { (A) } 8 \\\\ \hline \text { II } & \text { length of latus rectum } & \text { (B) }\left(\frac{29}{10}, \frac{-38}{10}\right) \\\\ \hline \text { III } & \text { Directrix } & \text { (C) } 3 x+4 y-1=0 \\\\ \hline \text { IV } & \begin{array}{l} \text { One end of the latus } \\\\ \text { rectum } \end{array} & \text { (D) }\left(\frac{-2}{5}, \frac{-16}{5}\right) \\\\ \hline \end{array} $$

    The correct answer is

A
I-B, II-E, III-C, IV-D
B
I-D, II-A, III-C, IV-B
C
I-B, II-A, III-C, IV-D
D
I-D, II-B, III-C, IV-A
2
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $\mathbf{A B}$ is the focal chord of the parabola $y^2=16 x$ and $A=(1,-4)$, then the equation of the normal to the parabola at the point $B$ is

A

$2 x+y-32=0$

B

$2 x+y-48=0$

C

$x-2 y+16=0$

D

$x+2 y-48=0$

3
TS EAMCET 2023 (Online) 14th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If one of the vertices of an equilateral triangle inscribed in the parabola $y^2=12 x$ coincides with the vertex of the parabola, then the area (in sq units) of that triangle is

A

$192 \sqrt{3}$

B

$864 \sqrt{3}$

C

$216 \sqrt{3}$

D

$432 \sqrt{3}$

4
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $x-2 y+k=0$ is a tangent to the parabola $y^2-4 x-4 y+8=0$, then the value of $k$ is

A

2

B

$2 / 5$

C

7

D

-7

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