1
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The normal at a point on the parabola $y^2=4 x$ passes through a point $P$. Two more normals to this parabola also pass through $P$. If the centroid of the triangle formed by the feet of these three normals is $G(2,0)$, then the abscissa of $P$ is

A

4

B

-4

C

5

D

-5

2
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

A normal chord $P Q$ drawn at a point $P$ on the parabola $y^2=5 x$ subtends a right angle at the vertex. If $P$ lies in the first quadrant, then the other end $Q$ of the normal chord is

A

$\left(\frac{5}{4}, \frac{5}{2}\right)$

B

$(5,-5)$

C

$(10,-5 \sqrt{2})$

D

$\left(\frac{5}{2}, \frac{5 \sqrt{2}}{2}\right)$

3
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $L(p, q), q>3$ is one end of the latus rectum of the parabola $(y-2)^2=3(x-1)$, then the equation of the tangent at $L$ to this parabola is

A

$2 x+y-7=0$

B

$4 x-4 y+7=0$

C

$2 x-y-3=0$

D

$2 x-3 y+7=0$

4
TG EAPCET 2025 (Online) 3rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The number of normals that can be drawn through the point $(2,0)$ to the parabola $y^2=7 x$ is

A

0

B

1

C

2

D

3

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