Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \...

Channel:
PW Solutions
Subscribers:
453,000
Published on ● Video Link: https://www.youtube.com/watch?v=Fm8AD_qeMbg


Duration: 9:25
0 views
0

Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \). The transverse and conjugate axes of this hyperbola coincide with the major and minor axes of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1 . Then
(a) The equation of the hyperbola is \( \frac{x^{2}}{9}-\frac{y^{2}}{16}=1 \)
(b) Ecentricity of the hyperbola is \( \frac{5}{3} \)
(c) The focus of the hyperbola is \( (5,0) \)
(d) The focus of the hyperbola is \( (5 \sqrt{3}, 0) \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


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 \( \quad \) Consider a hyperbola \( x y=4 \) and a line \( y+2 x=4, O \) is the ce...
2023-07-03Comprehension The vertices of a \( \triangle A B C \) lies on a rectangular hyperbola such that ...
2023-07-03Comprehension Consider a hyperbola: \( \frac{(x-7)^{2}}{a^{2}}-\frac{(y+3)^{2}}{b^{2}}=1 \). The...
2023-07-03Comprehension Consider a hyperbola: \( \frac{(x-7)^{2}}{a^{2}}-\frac{(y+3)^{2}}{b^{2}}=1 \). The...
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 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 \( y^{2}=12 x \), ...
2023-07-03Locus of the point of intersection of the tangents at the points with eccentric angles \( \phi \...
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
2023-07-03Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \...
2023-07-03Let a hyperbola passes through the focus of the ellipse \( \frac{x^{2}}{25}+\frac{y^{2}}{16}=1 \...
2023-07-03Let the eccentricity of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 \) be recipro...
2023-07-03Let the variable line \( y=k x+h \) is tangent to the hyperbola \( \frac{\mathrm{x}^{2}}{4}-\fra...
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...
2023-07-03At the point of intersection of the rectangular hyperbola \( x y=c^{2} \) and the parabola \( y^...
2023-07-03If the circle \( x^{2}+y^{2}=a^{2} \) intersects the hyperbola \( x y=c^{2} \) at four points \(...
2023-07-03The equation(s) to common tangent(s) to the two hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^...
2023-07-03If \( \frac{x}{a}+\frac{y}{b}=1 \) is a tangent to the curve \( x=4 t, y=\frac{4}{t}, t \in R \)...
2023-07-03If area of the triangle formed by latus rectum and tangents at the end points of latus rectum of...
2023-07-03If the distance between two parallel tangents having slope \( m \) drawn to the hyperbola \( \fr...