1
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
$a$ and $b$ are the semi-major and semi-minor axes of an ellipse whose axes are along the coordinate axes, If its latus rectum is of length 4 units and the distance between its foci is $4 \sqrt{2}$, then $a^{2}+b^{2}=$
A
24
B
18
C
16
D
12
2
TG EAPCET 2024 (Online) 10th May Evening Shift
MCQ (Single Correct Answer)
+1
-0
If the extremities of the latus recta having positive ordinate of the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a > b)$ lie on the parabola $x^{2}+2 a y-4=0$, then the points $(a, b)$ lie on the curve
A
$x y=4$
B
$x^{2}+y^{2}=4$
C
$\frac{x^{2}}{4}+\frac{y^{2}}{1}=1$
D
$\frac{x^{2}}{4}-\frac{y^{2}}{1}=1$
3
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
The length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is $\frac{8}{3}$. If the distance from the centre of the ellipse to its focus is $\sqrt{5}$, then $\sqrt{a^2+6 a b+b^2}=$
A
7
B
$12 \sqrt{2}$
C
$3 \sqrt{5}$
D
11
4
TG EAPCET 2024 (Online) 10th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$S$ is the focus of the ellips $\frac{x^2}{25}+\frac{y^2}{b^2}=1,(b<5)$ lying on the negative $X$-axis and $P(\theta)$ is a point on this ellipes. If the distance between the foci of this ellipse is 8 and $S^{\prime} P=7$, then $\theta=$
A
$\frac{\pi}{6}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{2 \pi}{3}$
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