1
AP EAPCET 2025 - 26th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $P(\alpha, \beta)$ is a point on the curve $9 x^2+4 y^2=144$ in the first quadrant and the minimum area of the triangle formed by the tangent of the curve at $P$ with the coordinate axis is $S$, then

A

$S=\sqrt{\alpha \beta}$

B

$S=\alpha \beta$

C

$S=2 \sqrt{\alpha \beta}$

D

$S=2 \alpha \beta$

2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse $9 x^2+4 y^2=72$ at the point $(2,3)$ with the $X$-axis is

A

$\frac{25}{2}$

B

$\frac{39}{4}$

C

$\frac{35}{4}$

D

$\frac{45}{4}$

3
AP EAPCET 2025 - 23rd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The equation of the normal drawn at the point $(\sqrt{2}+1,-1)$ to the ellipse $x^2+2 y^2-2 x+8 y+5=0$ is

A

$x+y=\sqrt{2}$

B

$x-2 y=3+\sqrt{2}$

C

$\sqrt{2} x-y=3+\sqrt{2}$

D

$2 x+y=2 \sqrt{2}+1$

4
AP EAPCET 2025 - 23rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If the tangents drawn from a point $P$ to the ellipse $4 x^2+9 y^2-16 x+54 y+61=0$ are perpendicular, then the locus of $P$ is
A

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

B

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

C

$x^2+y^2-6 x+4 y+9=0$

D

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

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