JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(\mathrm{P}(4,4 \sqrt{3})\) be a point on the parabola \(y^2=4 \mathrm{a} x\) and PQ be a focal chord of the parabola. If M and \(N\) are the foot of perpendiculars drawn from \(P\) and \(Q\) respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :
- A \(17 \sqrt{3}\)
- B \(\frac{263 \sqrt{3}}{8}\)
- C \(\frac{34 \sqrt{3}}{3}\)
- D \(\frac{343 \sqrt{3}}{8}\)
Answer & Solution
Correct Answer
(D) \(\frac{343 \sqrt{3}}{8}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (4,4 \sqrt{3}) \text { lies on } y^2=4 \mathrm{ax} \\ & \Rightarrow 48=4 \mathrm{a} \cdot 4 \\ & \quad 4 \mathrm{a}=12 \end{aligned}\) \(\Rightarrow y^2=12 x\) is equation of parabola Now, parameter of \(P\) is \(t_1=\frac{2}{\sqrt{3}} \Rightarrow\)…
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 the slope of the line \(45 x+5 y+3=0\) be \(27 r_1+\frac{9 r_2}{2} \quad\) for some \(r_1, \quad r_2 \in R\). Then \(\operatorname{Lim}_{x \rightarrow 3}\left(\int_3^\pi \frac{8 t^2}{\frac{3 r_2 x}{2}-r_2 x^2-r_1 x^3-3 x} d t\right)\) is equal to ...........JEE Mains 2024 Hard
- The number of real roots of the equation \(\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{4}\) is:JEE Mains 2021 Hard
- The slope of the line touching both the parabolas \({y^2} = 4x\) and \({x^2} = - 32y\), isJEE Mains 2014 Medium
- If the plane \(2x -y + 2z + 3 = 0\) has the distances \(\frac {1}{3}\) and \(\frac {2}{3}\) units from the planes \(4x -2y + 4z + \lambda = 0\) and \(2x -y + 2z + \mu = 0,\) respectively, then the maximum value of \(\lambda + \mu \) us equal toJEE Mains 2019 Hard
- Let \(A, B\) and \(C\) be sets such that \(\phi \ne A \cap B \subseteq C\). Then which of the following statements is not true ?JEE Mains 2019 Hard
- Let \(f(x)\) be a real differentiable function such that \(f(0)=1\) and \(f(x+y)=f(x) f^{\prime}(y)+f^{\prime}(x) f(y)\) for all \(x, y \in \mathbf{R}\). Then \(\sum_{\mathrm{n}=1}^{100} \log _{\mathrm{e}} f(\mathrm{n})\) is equal to :JEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(A\) and \(B\) be two invertible matrices of order \(3 \times 3\). If det \((ABA^T) = 8\) and \(det\,(AB^{-1}) = 8\), then \(det\, (BA^{-1} B^T)\) is equal toJEE Mains 2019 Hard
- Let \([t]\) denote the greatest integer \(\leq t\). The number of points where the function \(f(x)=[x]\left|x^{2}-1\right|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1], x \in(-2,2)\) is not continuous is ..... .JEE Mains 2021 Hard
- A group of students comprises of \(5\) boys and \(n\) girls. If the number of ways, in which a team of \(3\) students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is \(1750\), then \(n\) is equal toJEE Mains 2019 Hard
- Let the points \(\left(\frac{11}{2}, \alpha\right)\) lie on or inside the triangle with sides \(x+y=11, x+2 y=16\) and \(2 x+3 y=29\). Then the product of the smallest and the largest values of \(\alpha\) is equal to :JEE Mains 2025 Medium
- Let \(A = \{1, 2, 3, 4, 5, 6\}\). The number of one-one functions \(f: A \rightarrow A\) such that \(f(1) \geq 3\), \(f(3) \leq 4\) and \(f(2) + f(3) = 5\), is __________.JEE Mains 2026 Hard
- If non-zero real numbers \(b\) and \(c\) are such that \(min \,f\left( x \right) > \max \,g\left( x \right)\), where \(f\left( x \right) = {x^2} + 2bx + 2{c^2}\) and \(g\left( x \right) = {-x^2} - 2cx + {b^2}\)\(\left( {x \in R} \right)\); then \(\left| {\frac{c}{b}} \right|\) lies in the intervalJEE Mains 2014 Hard