A normal to the hyperbola \( \frac{x^{2}}{4}-\frac{y^{2}}{1}=1 \) has equal intercepts on the po...

Channel:
PW Solutions
Subscribers:
456,000
Published on ● Video Link: https://www.youtube.com/watch?v=HYYFX4VTDiE


Duration: 7:56
0 views
0

A normal to the hyperbola \( \frac{x^{2}}{4}-\frac{y^{2}}{1}=1 \) has equal intercepts on the positive \( x \)-axis and \( y \)-axis. If this normal touches the ellipse \( \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{~b}^{2}}=1 \). Then \( a^{2}+b^{2} \) is equal to:
(a) 5
(b) 25
(c) 16
(d) \( 25 / 3 \)
πŸ“²PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-03The ellipse \( 4 x^{2}+9 y^{2}=36 \) and the hyperbola \( a^{2} x^{2}-y^{2}= \) 4 intersect at r...
2023-07-03The locus of the foot of the perpendicular from the centre of the hyperbola \( x y=c^{2} \) on a...
2023-07-03If the tangent at the point \( (a \sec \alpha, b \tan \alpha) \) to the hyperbola \( \frac{x^{2}...
2023-07-03Locus of the middle point of the parallel chords with gradient \( \mathrm{m} \) of the rectangul...
2023-07-03If the sum of the slopes of the normal from a point \( P \) to the hyperbola \( x y=c^{2} \) is ...
2023-07-03If the angle between the asymptotes of hyperbola \( \frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}-\frac{...
2023-07-03The center of a rectangular hyperbola lies on the line \( y=2 x \). If one of the asymptotes is ...
2023-07-03If the foci of a hyperbola lie on \( y=x \) and one of the asymptotes is \( y=2 x \), then the e...
2023-07-03The equation of the chord joining two points \( \left(x_{1}, y_{1}\right) \) and \( \left(x_{2}\...
2023-07-03If the normal to the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) at any point \( P...
2023-07-03A normal to the hyperbola \( \frac{x^{2}}{4}-\frac{y^{2}}{1}=1 \) has equal intercepts on the po...
2023-07-03The number of points on the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=3 \) from which...
2023-07-03The equation of a common tangent with positive slope to the circle \( x^{2}+y^{2}-8 x=0 \) as we...
2023-07-03The locus of a point whose chord of contact with respect to the circle \( x^{2}+y^{2}=4 \) is a ...
2023-07-03If a variable line has its intercepts on the coordinate axis \( e \) and \( e^{\prime} \) where ...
2023-07-03Let \( L L^{\prime} \) be the latus rectum through the focus of the hyperbola \( \frac{x^{2}}{a^...
2023-07-03If the values of \( m \) for which the line \( y=m x+2 \sqrt{5} \) touches the hyperbola \( 16 x...
2023-07-03The equations of the transverse and conjugate axis of a hyperbola are, respectively, \( x+2 y-3=...
2023-07-03The asympote of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) from with any tang...
2023-07-03The equation of the transverse axis of the hyperbola \( (x-3)^{2}+(y+1)^{2}=(4 x+3 y)^{2} \) is:...
2023-07-03The locus of the middle points of chords of hyperbola \( 3 x^{2} \) \( -2 y^{2}+4 x-6 y=0 \) par...