JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(a\) and \(b\) be any two numbers satisfying \(\frac{1}{{{a^2}}} + \frac{1}{{{b^2}}} = \frac{1}{4}\). Then, the foot of perpendicular from the origin on the variable line, \(\frac{x}{a} + \frac{y}{b} = 1\) , lies on
- A a hyperbola with each semi-axis \( = \sqrt 2 \)
- B a hyperbola with each semi-axis \(= 2\)
- C a circle of radius \(= 2\)
- D a circle of radius \( = \sqrt 2 \)
Answer & Solution
Correct Answer
(C) a circle of radius \(= 2\)
Step-by-step Solution
Detailed explanation
Let the foot of the perpendicular from \((0,0)\) on the variable line \(\frac{x}{a} + \frac{y}{b} = 1\,\) is \(\left( {{x_1} > {y_1}} \right)\) Hence, perpendicular distance of the variable line \(\frac{x}{a} + \frac{y}{b} = 1\,\,\) from the point \(O\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the sum of first \(11\) terms of an \(A.P.\), \(a_{1} a_{2}, a_{3}, \ldots\)is \(0\left(\mathrm{a}_{1} \neq 0\right),\) then the sum of the \(A.P.\), \(a_{1}, a_{3}, a_{5}, \ldots, a_{23}\) is \(k a_{1},\) where \(k\) is equal toJEE Mains 2020 Hard
- Let \([ t ]\) denotes the greatest integer \(\leq t\). Then \(\frac{2}{\pi} \int \limits_{\pi / 6}^{5 \pi / 6}(8[\operatorname{cosec} x]-5[\cot x]) d x\) is equal toJEE Mains 2023 Hard
- For \(10\) observations \(x_1, x_2, \ldots, x_{10}\), if \(\sum_{i=1}^{10}(x_i+2)^2=180\) and \(\sum_{i=1}^{10}(x_i-1)^2=90\), then their standard deviation is:JEE Mains 2026 Medium
- In a group of \(400\) people, \(160\) are smokers and nonvegetarian; \(100\) are smokers and vegetarian and the remaining \(140\) are non-smokers and vegetarian. Their chances of getting a particular chest disorder are \(35\, \%, 20 \,\%\) and \(10 \,\%\) respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is ...... .JEE Mains 2021 Medium
- With the usual notation, in \(\Delta ABC\), if \(\angle A + \angle B = {120^o}\), \(a = \sqrt 3 - 1\), then the ratio \(\angle A : \angle B\), isJEE Mains 2019 Hard
- The product of the roots of the equation \(9 x^{2}-18|x|+5=0,\) isJEE Mains 2020 Medium
More PYQs from JEE Mains
- If two lines \(L_1\) and \(L_2\) in space, are defined by \({L_1} = \{ x = \sqrt \lambda y + \left( {\sqrt \lambda - 1} \right),z = \left( {\sqrt \lambda - 1} \right)y + \sqrt \lambda \} \) and \({L_2} = \{ x = \sqrt \mu y + \left( {1 - \sqrt \mu } \right),z = \left( {1 - \sqrt \mu } \right)y + \sqrt \mu \} \) then \(L_1\) is perpendicular to \(L_2\), for all non-negative reals \(\lambda \) and \( \mu \), such thatJEE Mains 2013 Hard
- The curve satisfying the differential equation, \(ydx-(x + 3y^2 )\, dy = 0\) and passing through the point \((1, 1)\) , also passes through the pointJEE Mains 2017 Hard
- For real numbers \(\alpha\) and \(\beta \neq 0\), if the point of intersection of the straight lines \(\frac{x-\alpha}{1}=\frac{y-1}{2}=\frac{z-1}{3}\) and \(\frac{x-4}{\beta}=\frac{y-6}{3}=\frac{z-7}{3}\) lies on the plane \(x+2 y-z=8\), then \(\alpha-\beta\) is equal to:JEE Mains 2021 Medium
- \(\int \limits_{-\pi}^{\pi}|\pi-| x || d x\) is equal to :JEE Mains 2020 Medium
- The value of \(\cos \,\frac{\pi }{{{2^2}}}.\cos \,\frac{\pi }{{{2^3}}}{._{..................}}.\cos \,\frac{\pi }{{{2^{10}}}}.\,\sin \,\frac{\pi }{{{2^{10}}}}\) isJEE Mains 2019 Hard
- Let \(\vec{a}=3 \hat{i}+\hat{j}\) and \(\vec{b}=\hat{i}+2 \hat{j}+\hat{k}\). Let \(\vec{c}\) be a vector satisfying \(\vec{a} \times(\vec{b} \times \vec{c})=\vec{b}+\lambda \vec{c}\). If \(\vec{b}\) and \(\vec{c}\) are non-parallel, then the value of \(\lambda\) is.JEE Mains 2022 Medium