For a given parabola \( y^{2}=4 a x \) two variable chords \( P Q \) and \( R S \) at right angl... VIDEO
For a given parabola \( y^{2}=4 a x \) two variable chords \( P Q \) and \( R S \) at right angles are drawn through the fixed point \( A\left(x_{1}\right. \), \( y_{1} \) ) inside the parabola, making variable angles \( \theta \) and \( \alpha \) with \( x \)-axis. If \( r_{1}, r_{2}, r_{3}, r_{4} \) are distances of \( P, Q, R \) and \( S \) from \( A \), then the value of \( \frac{1}{r_{1} r_{2}}+\frac{1}{r_{3} r_{4}} \)
(a) Independent of \( \theta \)
(b) Independent of \( \alpha \)
(c) Depends upon both \( \theta \) and \( \alpha \)
(d) Is a constant
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2023-07-08 Which of the following statements is/are correct?
(a) Reversible adiabatic process is an isoentr... 2023-07-08 Which of the following is(are) endothermic reaction?
(a) Combustion of methane.
(b) Decompositio... 2023-07-08 The normal boiling point of a liquid \( \mathrm{X} \) is \( 400 \mathrm{~K} \). Which of the f... 2023-07-08 If ends of latus rectum of parabola \( (x+1)^{2}=4(y+1) \) are vertices of an ellipse whose ecce... 2023-07-08 A circle \( S \) is described on the focal chord of the parabola \( y^{2}=4 x \) as diameter. ... 2023-07-08 Match the columns:
(a) \( \mathrm{A} \rightarrow \mathrm{r} ; \mathrm{B} \rightarrow \mathrm{p} ... 2023-07-08 Le \( m_{1}, m_{2}, m_{3}\left(m_{1}m_{2}m_{3}\right) \) be the slopes of the distinct normal to... 2023-07-08 \( A B \) and \( C D \) are two equal and parallel chords of the ellipse
\( \frac{x^{2}}{a^{2}}+... 2023-07-08 If one of the member of the orthogonal trajectory of \( y^{2}=k x \) where \( k \) is a paramete... 2023-07-08 The locus of feet of perpendicular from either foci of the ellipse \( (x-y+1)^{2}+(2 x+2 y-6)^{2... 2023-07-08 For a given parabola \( y^{2}=4 a x \) two variable chords \( P Q \) and \( R S \) at right angl... 2023-07-08 Through the vertex \( O \) of parabola \( y^{2}=4 x \), chords \( O P \) and \( O Q \) are drawn... 2023-07-08 Three normals to \( y^{2}=4 x \) pass through the point \( (15,12) \). Show that one of the norm... 2023-07-08 The tangent and normal at the point \( P\left(a t^{2}, 2 a t\right) \) to the parabola \( y^{2}=... 2023-07-08 Comprehension
Let \( M=\left\{(x, y) R \times R: x^{2}+\right. \) \( \left.y^{2} \leq r^{2}\righ... 2023-07-08 A circle of radius 2 units passes through the vertex and the focus of the parabola \( y^{2}=2 x ... 2023-07-08 Let \( P_{1} \) be a parabola with vertex \( (3,2) \) and focus \( (4,4) \) and \( P_{2} \) be i... 2023-07-08 Let \( S=\left\{(x \cdot y): x^{2}+y^{2}-6 x-8 y+21 \leq 0\right\} \)
\begin{tabular}{|l|l|l|l|}... 2023-07-08 The points on the axis of the parabola \( x^{2}+2 x+4 y+13= \) 0 from the where three distinct n... 2023-07-08 Let \( K \) denotes the square of the diameter of the circle whose diameter is the common chord ... 2023-07-08 Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+y^{2} \leq r^{2}\right\} \),
where \( r0 ...