Download App

STD 11 - 10.2 parabola,ellipse,hyperbola — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 10.2 parabola,ellipse,hyperbola1 Mark
MCQ
$P(6, 3)$ is a point on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ . If the normal at point $P$ intersect the $x-$ axis at $(10, 0)$ , then the eccentricity of the hyperbola is
  • ✓
    $\sqrt {\frac{5}{3}} $
  • B
    $\frac{{\sqrt {13} }}{3}$
  • C
    $\sqrt {\frac{5}{2}} $
  • D
    $\frac{{\sqrt {13} }}{2}$
✓

Answer

Correct option: A.
$\sqrt {\frac{5}{3}} $
a
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$

Slope of normal is $-\frac{a^{2}}{2 b^{2}}$

$\therefore$ Equation of normal at $\mathrm{P}(6,3)$ is

$y-3=-\frac{a^{2}}{2 b^{2}}(x-6)$

at $(10,0) \Rightarrow-3=-\frac{a^{2}}{2 b^{2}}(10-6)$

$\Rightarrow \quad \frac{3}{2}=\frac{a^{2}}{b^{2}}$

$\therefore \quad e^{2}=1+\frac{b^{2}}{a^{2}}=1+\frac{2}{3}=\frac{5}{3}$

$\therefore \quad e=\sqrt{\frac{5}{3}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 11 - 10.2 parabola,ellipse,hyperbola→STD 11 - 10.2 parabola,ellipse,hyperbola — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

$\mathop {\lim }\limits_{x \to 0} \,\frac{{x\,\cot \,\left( {4x} \right)}}{{{{\sin }^2}\,x\,{{\cot }^2}\,\left( {2x} \right)}}$ is equal to
→
Let the tangent drawn to the parabola $y ^{2}=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x$ $+2 y=5$. Then the normal to the hyperbola $\frac{x^{2}}{\alpha^{2}}-\frac{y^{2}}{\beta^{2}}=1$ at the point $(\alpha+4, \beta+4)$ does $NOT$ pass through the point.
→
The set of all $a \in R$ for which the equation $x | x -1|+| x +2|+a=0$ has exactly one real root is:
→
In set-builder method the null set is represented by:
→
Which of the following relation is a function?
→
If the $1011^{\text {th }}$ term from the end in the binomial expansion of $\left(\frac{4 x}{5}-\frac{5}{2 x }\right)^{2022}$ is 1024 times $1011^{\text {th }}$ term from the beginning, then $|x|$ is equal to
→
$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3.$ Then, $R^{-1}$ is:
→
What is the value of the $\lim_{\text{x} \rightarrow 5}\frac{32\text{x}+1}{\text{x} ^2-5\text{x}} ?$
→
Consider the set $A$ of natural numbers $n$ whose units digit is non-zero, such that if this units digit is erased, then the resulting number divides $n$. If $K$ is the number of elements in the set $A$, then
→
If $A$ and $B$ are two fixed points in a plane and $P$ is another variable point such that $P{A^2} + P{B^2} = $ constant, then the locus of the point $P$ is
→