Home
Class 12
MATHS
Let P(6,3) be a point on the hyperbola p...

Let P(6,3) be a point on the hyperbola parabola `x^2/a^2-y^2/b^2=1`If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

Text Solution

Verified by Experts

Normal at (6, 3) to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is
`(a^(2)x)/(6)+(b^(2)y)/(3)=a^(2)+b^(2)`
It passes through (9,0).
`therefore" "(9a^(2))/(6)=a^(2)+b^(2)`
`rArr" "(b^(2))/(a^(2))=(1)/(2)`
`rArr" "e^(2)-1=(1)/(2)`
`therefore" "e=sqrt((3)/(2))`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.1|3 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.2|12 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1 . If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is 2 (b) sqrt(2) (c) 3 (d) sqrt(3)

If the normal at a pont P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets the x-axis at G , show that the SG = eSP.S being the focus of the hyperbola.

let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal to that of the ellipse x^2+4y^2=4. if the hyperbola passes through a focus of the ellipse then: (a) the equation of the hyperbola is x^2/3-y^2/2=1 (b) a focus of the hyperbola is (2,0) (c) the eccentricity of the hyperbola is sqrt(5/3) (d) the equation of the hyperbola is x^2-3y^2=3

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

Let 'p' be the perpendicular distance from the centre C of the hyperbola x^2/a^2-y^2/b^2=1 to the tangent drawn at a point R on the hyperbola. If S & S' are the two foci of the hyperbola, then show that (RS + RS')^2 = 4 a^2(1+b^2/p^2) .

P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot

If the ellipse x^(2)+2y^(2)=4 and the hyperbola S = 0 have same end points of the latus rectum, then the eccentricity of the hyperbola can be

P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

If hyperbola (x^2)/(b^2)-(y^2)/(a^2)=1 passes through the focus of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then find the eccentricity of hyperbola.