Q. 11 F5.0( 1 Vote )
In each of the following find the equations of the hyperbola satisfying the given conditions
foci
, the latus-rectum = 8
Answer :
Given: Foci and the latus-rectum = 8
To find: equation of the hyperbola
Formula used:
The standard form of the equation of the hyperbola is,
Coordinates of the foci for a standard hyperbola is given by (±ae, 0)
Length of latus rectum is
According to the question:
We know,
b2 = a2(e2 – 1)
⇒ 4a = 45 – a2
⇒ a2 + 4a – 45 = 0
⇒ a2 + 9a – 5a – 45 = 0
⇒ a(a + 9) – 5(a + 9) = 0
⇒ (a + 9)(a – 5) = 0
⇒ a = -9 or a = 5
Since a is a distance, and it can’t be negative
⇒ a = 5
⇒ a2 = 25
b2 = 4a
⇒ b2 = 4(5)
⇒ b2 = 20
Hence, equation of hyperbola is:
Rate this question :


The eccentricity of the conic 9x2 – 16y2 = 144 is
RD Sharma - MathematicsThe latus-rectum of the hyperbola 16x2 – 9y2 = 144 is
RD Sharma - MathematicsThe eccentricity of the hyperbola x2 – 4y2 = 1 is
RD Sharma - MathematicsThe foci of the hyperbola 2x2 – 3y2 = 5 are
RD Sharma - MathematicsThe equation of the conic with focus at (1, -1) directrix along x – y + 1= 0 and eccentricity is
The equation of the hyperbola whose centre is (6, 2) one focus is (4, 2) and of eccentricity 2 is
RD Sharma - MathematicsThe eccentricity the hyperbola is
A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA – PB = k(k ≠ 0), then the locus of P is
RD Sharma - MathematicsThe equation of the hyperbola whose foci are (6, 4) and (-4, 4) and eccentricity 2, is
RD Sharma - MathematicsThe length of the straight line x – 3y = 1 intercepted by the hyperbola x2 – 4y2 = 1 is
RD Sharma - Mathematics