If a variable line has its intercepts on the coordinate axis \( e \) and \( e^{\prime} \) where ...

Channel:
PW Solutions
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=e5NlCIUP6uE


Duration: 10:03
4 views
0

If a variable line has its intercepts on the coordinate axis \( e \) and \( e^{\prime} \) where \( \frac{\mathrm{e}}{2} \) and \( \frac{e^{\prime}}{2} \) are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle \( x^{2}+ \) \( y^{2}=r^{2} \), where \( r= \)
(a) 1
(b) 2
(c) 3
(d) Cannot be decided
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-03(i) Let \( z_{1}=1+i \) and \( z_{2}=-1- \) i. Find \( z_{3} \in C \) such that triangle \( z_{1...
2023-07-03Let the foci of the ellipe \( \frac{x^{2}}{16}+\frac{y^{2}}{7}=1 \) and the hyperbola \( \frac{x...
2023-07-03An ellipse and a hyperbola have their principal axes along the coordinate axes and have a common...
2023-07-03Write equation of straight line which makes angle \( 60^{\circ} \) and passing through point \( ...
2023-07-03If the line \( x-1=0 \), is a directrix of the hyperbola \( k x^{2}-y^{2} \) \( =6 \), then the ...
2023-07-03The number of normal(s) to rectangular hyperbola which can touch its conjugate is equal to
2023-07-03Tangent are drawn from any point on the hyperbola \( x^{2} / 9- \) \( y^{2} / 4=1 \) to the circ...
2023-07-03Tangents are drawn from any point on the hyperbola \( 4 x^{2}-9 y^{2}=36 \) to the circle \( x^{...
2023-07-03If \( x+y=3 \) is tangent at \( (2,1) \) on hyperbola, intersects asymptotes at \( A \) and \( B...
2023-07-03A common tangent \( T \) to the curves \( C_{1}: \frac{x^{2}}{4}+\frac{y^{2}}{9}=1 \) and \( C_{...
2023-07-03If a variable line has its intercepts on the coordinate axis \( e \) and \( e^{\prime} \) where ...
2023-07-03Comprehension Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hype...
2023-07-03The normal at one extrimity of latus rectum (in 1st quadrant) of the ellipse \( \frac{x^{2}}{a^{...
2023-07-03Which of the following pairs of ellipse and hyperbola are orthogonal (a) \( \frac{x^{2}}{100}+\f...
2023-07-03Comprehension The vertices of a \( \triangle A B C \) lies on a rectangular hyperbola such that ...
2023-07-03Consider the hyperbola \( H: x^{2}-y^{2}=1 \) and a circle \( \mathrm{S} \) with center \( N\lef...
2023-07-03The minimum value of \( (\tan A-\cos \mathrm{B})^{2}+(\cot A-\sin B)^{2} \), where \( A \) and \...
2023-07-03Comprehension \( \quad \) Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the ce...
2023-07-03Three points \( A, B \) and \( C \) are taken on rectangular hyperbola \( x y=4 \) where \( B(-2...
2023-07-03Comprehension The vertices of a \( \triangle A B C \) lies on a rectangular hyperbola such that ...
2023-07-03Comprehension Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hype...