For a given parabola \( y^{2}=4 a x \) two variable chords \( P Q \) and \( R S \) at right angl...

Channel:
Subscribers:
443,000
Published on ● Video Link: https://www.youtube.com/watch?v=LQUH_cm_Y9Q



Duration: 14:34
7 views
0


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


2023-07-08Which of the following statements is/are correct? (a) Reversible adiabatic process is an isoentr...
2023-07-08Which of the following is(are) endothermic reaction? (a) Combustion of methane. (b) Decompositio...
2023-07-08The normal boiling point of a liquid \( \mathrm{X} \) is \( 400 \mathrm{~K} \). Which of the f...
2023-07-08If ends of latus rectum of parabola \( (x+1)^{2}=4(y+1) \) are vertices of an ellipse whose ecce...
2023-07-08A circle \( S \) is described on the focal chord of the parabola \( y^{2}=4 x \) as diameter. ...
2023-07-08Match the columns: (a) \( \mathrm{A} \rightarrow \mathrm{r} ; \mathrm{B} \rightarrow \mathrm{p} ...
2023-07-08Le \( m_{1}, m_{2}, m_{3}\left(m_{1}m_{2}m_{3}\right) \) 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}}+...
2023-07-08If one of the member of the orthogonal trajectory of \( y^{2}=k x \) where \( k \) is a paramete...
2023-07-08The locus of feet of perpendicular from either foci of the ellipse \( (x-y+1)^{2}+(2 x+2 y-6)^{2...
2023-07-08For a given parabola \( y^{2}=4 a x \) two variable chords \( P Q \) and \( R S \) at right angl...
2023-07-08Through the vertex \( O \) of parabola \( y^{2}=4 x \), chords \( O P \) and \( O Q \) are drawn...
2023-07-08Three normals to \( y^{2}=4 x \) pass through the point \( (15,12) \). Show that one of the norm...
2023-07-08The tangent and normal at the point \( P\left(a t^{2}, 2 a t\right) \) to the parabola \( y^{2}=...
2023-07-08Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+\right. \) \( \left.y^{2} \leq r^{2}\righ...
2023-07-08A circle of radius 2 units passes through the vertex and the focus of the parabola \( y^{2}=2 x ...
2023-07-08Let \( P_{1} \) be a parabola with vertex \( (3,2) \) and focus \( (4,4) \) and \( P_{2} \) be i...
2023-07-08Let \( S=\left\{(x \cdot y): x^{2}+y^{2}-6 x-8 y+21 \leq 0\right\} \) \begin{tabular}{|l|l|l|l|}...
2023-07-08The points on the axis of the parabola \( x^{2}+2 x+4 y+13= \) 0 from the where three distinct n...
2023-07-08Let \( K \) denotes the square of the diameter of the circle whose diameter is the common chord ...
2023-07-08Comprehension Let \( M=\left\{(x, y) R \times R: x^{2}+y^{2} \leq r^{2}\right\} \), where \( r0 ...