Download App

10.2 parabola,ellipse,hyperbola — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.2 parabola,ellipse,hyperbola1 Mark
MCQ
The values of parameter $'a'$ such that the line $\left( {{{\log }_2}\left( {1 + 5a - {a^2}} \right)} \right)x - 5y - \left( {{a^2} - 5} \right) = 0$ is a normal to the curve $xy = 1$ , may lie in the interval
  • A
    $\left( { - \infty ,0} \right)$
  • ✓
    $(0, 5)$
  • C
    $(5, 10)$
  • D
    $\left( {10,\infty } \right)$
✓

Answer

Correct option: B.
$(0, 5)$
b
Given curve is $y=\frac{1}{x} $

$\Rightarrow \frac{d y}{d x}=-\frac{1}{x^{2}}$

$\therefore $ slope of normal $\left.=x^{2}>0 \text { (As } x \neq 0\right)$

$\therefore $ slope of given line $=\frac{\log _{2}\left(1+5 a-a^{2}\right)}{5}>0$

$\Rightarrow \log _{2}\left(1+5 \mathrm{a}-\mathrm{a}^{2}\right)>0 $

$\Rightarrow 1+5 \mathrm{a}-\mathrm{a}^{2}>1$

$\Rightarrow a^{2}-5 a<0$

Hence $a$ $\in(0,5)$

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 "MCQ" from 10.2 parabola,ellipse,hyperbola→10.2 parabola,ellipse,hyperbola — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Radius of circle touching $y-$axis at point $P(0,2)$ and circle $x^2 + y^2 = 16$ internally-
→
Among all cyclic quadrilaterals inscribed in a circle of radius $R$ with one of its angles equal to $120^{\circ}$. Consider the one with maximum possible area. Its area is
→
If $\text{f(x)}=\log\Big(\frac{1+\text{x}}{1-\text{x}}\Big),$ then $\text{f}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ is equal to:
→
The number of irrational terms in the expansion of $\Big(4^{\frac{1}{5}}+7^{\frac{1}{10}}\Big)^{45}$ is:
→
If $a^3 + b^6 = 2$, then the maximum value of the term independent of $x$ in the expansion of  $(ax^{\frac{1}{3}}+bx^{\frac{-1}{6}})^9$ is, where $(a > 0, b > 0)$
→
Let the eccentricity of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be reciprocal to that of the ellips $x^2+4 y^2=4$. If the hyperbola passes through a focus of the ellipse, then

$(A)$ the equation of the hyperbola is $\frac{x^2}{3}-\frac{y^2}{2}=1$

$(B)$ a focus of the hyperbola is $(2,0)$

$(C)$ the eccentricity of the hyperbola is $\sqrt{\frac{5}{3}}$

$(D)$ the equation of the hyperbola is $x^2-3 y^2=3$

→
If the equation $p{x^2} + (2 - q)xy + 3{y^2}$ $ - 6qx + 30y + 6q = 0$ represents a circle, then the values of $p$ and $q$ are
→
If $\mathop {\lim }\limits_{n \to \infty } \frac{{1 - {{(10)}^n}}}{{1 + {{(10)}^{n + 1}}}} = \frac{{ - \alpha }}{{10}}$, then give the value of $\alpha $ is
→
The remainder, when $7^{103}$ is divided by $17$ is $..........$.
→
The positive integer just greater than $(1 + 0.0001)^{10000}$ is
→