JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Two parabolas have the same focus \((4,3)\) and their directrices are the \(x\)-axis and the \(y\)-axis, respectively. If these parabolas intersects at the points \(A\) and \(B\), then \((A B)^2\) is equal to :
- A 392
- B 384
- C 192
- D 96
Answer & Solution
Correct Answer
(C) 192
Step-by-step Solution
Detailed explanation
The parabolas are \((x-4)^2+(y-3)^2=x^2\) ...(i) and \((x-4)^2+(y-3)^2=y^2\)... If point of intersection are \(A\left(x_1, y_1\right)\) and \(B\left(x_2, y_2\right)\) By solving (i) and (ii), we get…
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
- Statement \(-1 :\) The value of the integral \(\mathop \smallint \limits_{\frac{\pi }{6}}^{\frac{\pi }{3}} \frac{{dx}}{{1 + \sqrt {\tan x} }} = \frac{\pi }{6}\) Statement \(-2 :\) \(\;\mathop \smallint \limits_a^b {\rm{f}}\left( {\rm{x}} \right)dx = \mathop \smallint \limits_a^b {\rm{f}}\left( {a + b - x} \right)\;dx\)JEE Mains 2013 Medium
- If for \(a >0,\) the feet of perpendiculars from the points \(A ( a ,-2 a , 3)\) and \(B (0,4,5)\) on the plane \(l x+m y+n z=0\) are points \(C(0,-a,-1)\) and \(D\) respectively, then the length of line segment \(CD\) is equal toJEE Mains 2021 Hard
- The image of the line \(\frac{{x - 1}}{3} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - 5}}\) in the plane \(2x - y + z + 3 = 0\) is the line :JEE Mains 2014 Hard
- The integral \(\int \limits_{0}^{2} \| x-1|-x| d x\) is equal toJEE Mains 2020 Hard
- The sum of the real values of \(x\) for which the middle term in the binomial expansion of \({\left( {\frac{{{x^3}}}{3} + \frac{3}{x}} \right)^8}\) equals \(5670\) isJEE Mains 2019 Hard
- Let the circle \(C_1: x^2+y^2-2(x+y)+1=0\) and \(C_2\) be a circle having centre at \((-1,0)\) and radius \(2\) . If the line of the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) intersects the \(\mathrm{y}\)-axis at the point \(\mathrm{P}\), then the square of the distance of \(\mathrm{P}\) from the centre of \(\mathrm{C}_1\) is :JEE Mains 2024 Hard
More PYQs from JEE Mains
- If \(|x|<1,|y|<1\) and \(x \neq y,\) then the sum to infinity of the following series \((x+y)+\left(x^{2}+x y+y^{2}\right)+\left(x^{3}+x^{2} y+x y^{2}+y^{3}\right)+\ldots .\)JEE Mains 2020 Medium
- Let \({f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\) where \(x \in R\;\) and \(k \ge 1\). Then \({f_4}\left( x \right) - {f_6}\left( x \right) \) is equalsJEE Mains 2014 Hard
- The value of \(36(4 \cos ^2 9^{\circ}-1)(4 \cos ^2 27^{\circ}-1) (4\cos ^2 81^{\circ}-1) (4 \cos ^2 243^{\circ}-1)\) isJEE Mains 2023 Hard
- Let \(A\) and \(B\) be two events such that \(P ( B \mid A )=\frac{2}{5}\), \(P ( A \mid B )=\frac{1}{7}\) and \(P ( A \cap B )=\frac{1}{9} .\) Consider \(( S 1) P \left( A ^{\prime} \cup B \right)=\frac{5}{6}\) \(( S 2) P \left( A ^{\prime} \cap B ^{\prime}\right)=\frac{1}{18}\). Then.JEE Mains 2022 Hard
- Let A be the focus of the parabola \(y^{2}=8x.\) Let the line \(y=mx+c\) intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is \((\frac{7}{3},\frac{4}{3})\) , then \((BC)^{2}\) is equal to:JEE Mains 2026 Medium
- Let the sum of the first three terms of an \(A. P,\) be \(39\) and the sum of its last four terms be \(178.\) If the first term of this \(A.P.\) is \(10,\) then the median of the \(A.P.\) isJEE Mains 2015 Hard