JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of a point which divides the line segment joining the point \((0,-1)\) and a point on the parabola, \(\mathrm{x}^{2}=4 \mathrm{y},\) internally in the ratio \(1: 2,\) is
- A \(9 x^{2}-3 y=2\)
- B \(9 x^{2}-12 y=8\)
- C \(x^{2}-3 y=2\)
- D \(4 x^{2}-3 y=2\)
Answer & Solution
Correct Answer
(B) \(9 x^{2}-12 y=8\)
Step-by-step Solution
Detailed explanation
\(\Rightarrow 3 \mathrm{h}=2 \mathrm{t}\) and \(3 \mathrm{k}=\mathrm{t}^{2}-2\) \(\Rightarrow 3 \mathrm{y}=\left(\frac{3 \mathrm{x}}{2}\right)^{2}-2 \)\(\Rightarrow 12 \mathrm{y}=9 \mathrm{x}^{2}-8\)
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
- Let \(g(x)=f(x)+f(1-x)\) and \(f^{\prime \prime}(x) > 0, x \in(0,1)\). If \(g\) is decreasing in the interval \((0, \alpha)\) and increasing in the interval \((\alpha, 1)\), then \(\tan ^1(2 \alpha)+\tan ^{-1}\left(\frac{1}{\alpha}\right)+\tan ^{-1}\left(\frac{\alpha+1}{\alpha}\right)\) is equal to :JEE Mains 2023 Hard
- The number of \(4\) letter words (with or without meaning) that can be formed from the eleven letters of the word \('EXAMINATION'\) isJEE Mains 2020 Hard
- The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , isJEE Mains 2025 Medium
- Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+\beta \hat{\mathrm{k}}, \alpha, \beta \in \mathrm{R}\). Let a vector \(\overrightarrow{\mathrm{b}}\) be such that the angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{\pi}{4}\) and \(|\vec{b}|^2=6\), If \(\vec{a} \cdot \vec{b}=3 \sqrt{2}\), then the value of \(\left(\alpha^2+\beta^2\right)|\vec{a} \times \vec{b}|^2\) is equal toJEE Mains 2024 Hard
- If \(\cot ^{-1}(\alpha)=\cot ^{-1} 2+\cot ^{-1} 8+\cot ^{-1} 18\) \(+\cot ^{-1} 32+\ldots . .\) upto \(100\) terms, then \(\alpha\) isJEE Mains 2021 Hard
- The coefficient of \(x^{-5}\) in the binomial expansion of \({\left( {\frac{{x + 1}}{{{x^{\frac{2}{3}}} - {x^{\frac{1}{3}}} + 1}} - \frac{{x - 1}}{{x - {x^{\frac{1}{2}}}}}} \right)^{10}}\) where \(x \ne 0, 1\) , isJEE Mains 2017 Hard
More PYQs from JEE Mains
- The number of points, where the function \(f: R \rightarrow R , f ( x )=| x -1| \cos | x -2| \sin | x -1|+\) \((x-3)\left|x^{2}-5 x+4\right|\), is NOT differentiable, is.JEE Mains 2022 Hard
- Let \(\mathrm{z}\) be a complex number such that \(|\mathrm{z}+2|=1\) and \(\operatorname{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}\). Then the value of \(|\operatorname{Re}(\overline{z+2})|\) is :JEE Mains 2024 Medium
- The slope of the line touching both the parabolas \({y^2} = 4x\) and \({x^2} = - 32y\), isJEE Mains 2014 Medium
- If the coefficient of \(x ^{15}\) in the expansion of \(\left(a x^3+\frac{1}{b x^{\frac{1}{3}}}\right)^{15}\) is equal to the coefficient of \(x^{-15}\) in the expansion of \(\left(a x^{\frac{1}{3}}-\frac{1}{b x^3}\right)^{15}\), where \(a\) and \(b\) are positive real numbers, then for each such ordered pair \((a, b) :\)JEE Mains 2023 Hard
- Let \(A\) be a \(2 \times 2\) matrix with real entries such that \(A ^{\prime}=\alpha A + I\), where \(\alpha \in R -\{-1,1\}\). If det \(\left(A^2-A\right)=4\), then the sum of all possible values of \(\alpha\) is equal toJEE Mains 2023 Hard
- Let \(f\) be a twice differentiable function such that \(f(x)=\int_{0}^{x}\tan(t-x)dt-\int_{0}^{x}f(t)\tan t\,dt\), \(x \in \left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)\). Then \(f''\left(\dfrac{\pi}{6}\right)+12f'\left(-\dfrac{\pi}{6}\right)+f\left(\dfrac{\pi}{6}\right)\) is equal to ______JEE Mains 2026 Hard