TG EAPCET 2025 (Online) 3rd May Morning Shift | Hyperbola Question 5 | Mathematics

If the tangent drawn at the point $P(3 \sqrt{2}, 4)$ on the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$ meets its directrix at $Q(\alpha, \beta)$ in fourth quadrant, then $\beta=$

$\frac{5 \sqrt{2}-9}{4}$

$-\frac{9}{5}$

$\frac{12 \sqrt{2}-20}{5}$

$-\frac{5}{4}$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

If $l$ is the maximum value of $-3 x^2+4 x+1$ and $m$ is the minimum value of $3 x^2+4 x+1$, then the equation of the hyperbola having foci at $(l, 0),(7 m, 0)$ and eccentricity as 2 is

$36 x^2-12 y^2=49$

$49 x^2-36 y^2=12$

$2 x^2-5 y^2=1$

$36 x^2-12 y^2=1$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

The curve represented by $\frac{x^2}{12-\alpha}+\frac{y^2}{\alpha-10}=1$ is

a hyperbola for some values of $\alpha$ in $(10,12)$

an ellipse for all values of $\alpha$ in $(10,12)$

a circle for some value of $\alpha$ in $(10,12)$

a hyperbola for all values of $\alpha$ in $(10,12)$

TG EAPCET 2025 (Online) 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

Let $x$ be the eccentricity of a hyperbola whose transverse axis is twice its conjugate axis. Let $y$ be the eccentricity of another hyperbola for which the distance between the focii is 3 times the distance between its directrices. Then $y^2-x^2=$

$\frac{23}{16}$

$\frac{7}{4}$

$\frac{4}{7}$

$\frac{16}{23}$

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