JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the normal at the point \(P\) on the parabola \(y ^{2}=\) \(6 x\) pass through the point \((5,-8)\). If the tangent at \(P\) to the parabola intersects its directrix at the point \(Q\), then the ordinate of the point \(Q\) is
- A \(-3\)
- B \(-\frac{9}{4}\)
- C \(-\frac{5}{2}\)
- D \(-2\)
Answer & Solution
Correct Answer
(B) \(-\frac{9}{4}\)
Step-by-step Solution
Detailed explanation
Equation of normal : \(y =- tx +2 at + at ^{3} \quad\left( a =\frac{3}{2}\right)\) since passing through \((5,-8)\), we get \(t=-2\) Co-ordinate of \(Q :(6,-6)\) Equation of tangent at \(Q : x +2 y +6=0\) Put \(x=\frac{-3}{2}\) to get \(R\left(\frac{-3}{2}, \frac{-9}{4}\right)\)
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
- The the circle passing through the foci of the \(\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1\) and having centre at \((0,3) \) isJEE Mains 2013 Medium
- If \(\frac{1}{2 \times 3 \times 4}+\frac{1}{3 \times 4 \times 5}+\frac{1}{4 \times 5 \times 6}+\ldots+\) \(\frac{1}{100 \times 101 \times 102}=\frac{ k }{101}\), then \(34\,k\) is equal to \(.....\)JEE Mains 2022 Hard
- If \((a, b, c)\) is the image of the point \((1,2,-3)\) in the line, \(\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1},\) then \(a+b+c\) is equal toJEE Mains 2020 Medium
- The equation of line passing through \((-4, 1, 3)\), parallel to the plane \(x + 2y - z - 5 = 0\) and intersecting the line \(\frac{{x + 1}}{{ - 3}} = \frac{{y - 3}}{2} = \frac{{z - 2}}{{ - 1}}\) isJEE Mains 2019 Hard
- The Coefficient of \(x ^{-6}\), in the expansion of \(\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9\), is \(........\).JEE Mains 2023 Hard
- \(\lim \limits_{x \rightarrow \frac{1}{\sqrt{2}}} \frac{\sin \left(\cos ^{-1} x\right)-x}{1-\tan \left(\cos ^{-1} x\right)}\) is equal toJEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(A=\begin{bmatrix} 1 & 2 & 7 \\ 4 & -2 & 8 \\ 3 & 8 & -7 \end{bmatrix}\) and \(\det(A-\alpha I)=0\), where \(\alpha\) is a real number. If the largest possible value of \(\alpha\) is \(p\), then the circle \((x-p)^2+(y-2p)^2=320\), intersects the co-ordinate axes atJEE Mains 2026 Hard
- All the points in the set \(S\, = \left\{ {\frac{{\alpha \, + \,i}}{{\alpha \, - \,i}}\,:\,\alpha \, \in \,R} \right\}\,(i\, = \,\sqrt { - 1} )\) lie on aJEE Mains 2019 Hard
- Let \(a _1, a _2, a _3, \ldots\) be a \(G.P.\) of increasing positive numbers. Let the sum of its \(6^{\text {th }}\) and \(8^{\text {th }}\) terms be \(2\) and the product of its \(3^{\text {rd }}\) and \(5^{\text {th }}\) terms be \(\frac{1}{9}\). Then \(6\left( a _2+\right.\) \(\left.a_4\right)\left(a_4+a_6\right)\) is equal toJEE Mains 2023 Hard
- Let the ellipse \(E: \frac{x^{2}}{144}+\frac{y^{2}}{169}=1\) and the hyperbola \(H:\frac{x^{2}}{16}-\frac{y^{2}}{\lambda^{2}}=-1\) have the same foci. If e and L respectively denote the eccentricity and the length of the latus rectum of H, then the value of \(24(e+L)\) is:JEE Mains 2026 Hard
- Let the plane \(2 x+3 y+z+20=0\) be rotated through a right angle about its line of intersection with the plane \(x-3 y+5 z=8\). If the mirror image of the point \(\left(2,-\frac{1}{2}, 2\right)\) in the rotated plane is \(B ( a , b , c )\), thenJEE Mains 2022 Hard
- Let \(\overrightarrow{\mathrm{a}}=3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{c}}\) be a vector such that \((\vec{a}+\vec{b}) \times \vec{c}=2(\vec{a} \times \vec{b})+24 \hat{j}-6 \hat{k}\) and \((\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}+\hat{\mathrm{i}}) \cdot \overrightarrow{\mathrm{c}}=-3\). Then \(|\overrightarrow{\mathrm{c}}|^2\) is equal to ...........JEE Mains 2024 Hard