Which of the following pairs of ellipse and hyperbola are orthogonal (a) \( \frac{x^{2}}{100}+\f...

Channel:
PW Solutions
Subscribers:
449,000
Published on ● Video Link: https://www.youtube.com/watch?v=deBl0wm8hGA


Duration: 12:59
0 views
0

Which of the following pairs of ellipse and hyperbola are orthogonal
(a) \( \frac{x^{2}}{100}+\frac{y^{2}}{64}=1 \) and \( \frac{x^{2}}{19}-\frac{y^{2}}{17}=1 \)
(b) \( \frac{x^{2}}{81}+\frac{y^{2}}{49}=1 \) and \( \frac{x^{2}}{17}-\frac{y^{2}}{15}=1 \)
(c) \( \frac{x^{2}}{64}+\frac{y^{2}}{36}=1 \) and \( \frac{x^{2}}{15}-\frac{y^{2}}{13}=1 \)
(d) \( \frac{x^{2}}{49}+\frac{y^{2}}{25}=1 \) and \( \frac{x^{2}}{13}-\frac{y^{2}}{11}=1 \)
๐Ÿ“ฒPW App Link - https://bit.ly/YTAI_PWAP
๐ŸŒPW Website - https://www.pw.live



Other Videos By PW Solutions


2023-07-03Three points \( A, B \) and \( C \) are taken on rectangular hyperbola \( x y=4 \) where \( B(-2...
2023-07-03Comprehension \( \quad \) Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the ce...
2023-07-03The normal at one extrimity of latus rectum (in 1st quadrant) of the ellipse \( \frac{x^{2}}{a^{...
2023-07-03Comprehension The vertices of a \( \triangle A B C \) lies on a rectangular hyperbola such that ...
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...
2023-07-03Comprehension Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hype...
2023-07-03Comprehension Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the centre of hype...
2023-07-03Comprehension Consider a hyperbola: \( \frac{(x-7)^{2}}{a^{2}}-\frac{(y+3)^{2}}{b^{2}}=1 \). The...
2023-07-03Comprehension \( \quad \) Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the ce...
2023-07-03Which of the following pairs of ellipse and hyperbola are orthogonal (a) \( \frac{x^{2}}{100}+\f...
2023-07-03Locus of the point of intersection of the tangents at the points with eccentric angles \( \phi \...
2023-07-03Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \...
2023-07-03The equation \( \frac{x^{2}}{29-p}+\frac{y^{2}}{4-p}=1(p \neq 4,29) \) represents (A) an ellipse...
2023-07-03If a variable chord of the hyperbola \( x^{2}-y^{2}=9 \) touches the parabola \( y^{2}=12 x \), ...
2023-07-03Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \...
2023-07-03The focal length of the hyperbola \( x^{2}-3 y^{2}-4 x-6 y-11=0 \), is (A) 4 (B) 6 (C) 8 (D) 10
2023-07-03Through the positive vertex of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) tan...
2023-07-03Let the variable line \( y=k x+h \) is tangent to the hyperbola \( \frac{\mathrm{x}^{2}}{4}-\fra...
2023-07-03Let the eccentricity of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) be recipro...
2023-07-03The lines parallel to the normal to the curve \( x y=1 \) is/are: (a) \( 3 x+4 y+5=0 \) (b) \( 3...