A vertical line passing through the point \( (h, 0) \) intersects the ellipse \( \frac{x^{2}}{4}... VIDEO
A vertical line passing through the point \( (h, 0) \) intersects the ellipse \( \frac{x^{2}}{4}+\frac{y^{2}}{3}=1 \) at the points \( P \) and \( Q \). If the tangents to the ellipse at \( P \) and \( Q \) meet at the point \( R \) If \( \Delta(h)= \) area of the \( \Delta P Q R, \Delta_{1}=\max _{1 / 2 \leq h \leq 1} \Delta(h) \) and \( \Delta_{2}=\min _{1 / 2 \leq h \leq 1} \Delta(h) \), then \( \frac{8}{\sqrt{5}} \Delta_{1}-8 \Delta_{2} \) is equal to [Integer Type Question, 2013 Adv.]
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2022-10-27 If \( f(x) \) is a cubic polynomial which has local maximum at \( x=-1 \). If \( f(2)=18, f(1)=-... 2022-10-27 Find a point on the curve \( x^{2}+2 y^{2}=6 \) whose distance from the line \( x+y=7 \), is min... 2022-10-27 Consider the function \( f:(-\infty, \infty) \rightarrow(-\infty, \infty) \) defined by \( f(x)=... 2022-10-27 Which of the following is true?
[Passage Based Question, 2008]
(a) \( f(x) \) is decreasing on \... 2022-10-27 If \( f(x)=x^{2}+2 b x+2 c^{2} \) and \( g(x)=-x^{2}-2 c x+b^{2} \),
such that \( \min f(x)\max ... 2022-10-27 The maximum value of \( \left(\cos \alpha_{1}\right) \cdot\left(\cos \alpha_{2}\right) \cdot \ld... 2022-10-27 The total number of local maxima and local minima of the function \( f(x)=\left\{\begin{array}{l... 2022-10-27 The second degree polynomial \( f(x) \), satisfying \( f(0)=0 \), \( f(1)=1, f^{\prime}(x)0 \for... 2022-10-27 A rectangular sheet of fixed perimeter with sides having their lengths in the ratio \( 8: 15 \) ... 2022-10-27 Let \( f, g \) and \( h \) be real-valued functions defined on the interval \( [0,1] \) by \( f(... 2022-10-27 A vertical line passing through the point \( (h, 0) \) intersects the ellipse \( \frac{x^{2}}{4}... 2022-10-27 The length of a longest interval in which the function \( 3 \sin x-4 \sin ^{3} x \) is increasin... 2022-10-27 If \( f(x)=x^{3}+b x^{2}+c x+d \) and \( 0b^{2}c \), then in
\( (-\infty, \infty) \) [One Correc... 2022-10-27 If the function \( g:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \) ... 2022-10-27 The function \( f(x)=2|x|+|x+2|-|| x+2|-2| x \| \) has a local minimum or a local maximum at \( ... 2022-10-27 If \( f(x)=(x-a)(x-b) \) for \( a, b \in R \), then minimum number of roots of equation
\( \pi\l... 2022-10-27 Let \( f: R \rightarrow(0, \infty) \) and \( g: R \rightarrow R \) be twice differentiable funct... 2022-10-27 The number of points in \( (-\infty, \infty) \) for which \( x^{2}-x \sin x-\cos x=0 \), is [One... 2022-10-27 If \( f:(0, \infty) \rightarrow R \) be given by \( f(x)=\int_{1 / x}^{x} e^{-\left(t+\frac{1}{t... 2022-10-27 Match the entries of the following two columns. 2022-10-27 The least value of \( a \) for which the equation, \( \frac{4}{\sin x}+\frac{1}{1-\sin x}=a \) h...