Home
Class 12
MATHS
Tangents are drawn to the hyperbola 3x^2...

Tangents are drawn to the hyperbola `3x^2-2y^2=25` from the point `(0,5/2)dot` Find their equations.

Text Solution

Verified by Experts

The correct Answer is:
`y=(5)/(2)pm(3)/(2)x`
The hyperbola is
`3x^(2)-2y^(2)=25`
`"or "(x^(2))/(25//3)-(y^(2))/(25//2)=1" (1)"`
Tangent to the hyperbola having slope m is
`y=mx+sqrt(a^(2)m^(2)-b^(2))" (2)"`
For the given hyperbola =, the tangent having slope m is
`y=mx+sqrt((25)/(3)m^(2)-(25)/(2))`
It passes through (0, 5/2). Therefore,
`(25)/(4)=(25)/(3)m^(2)-(25)/(2)`
`"or "(1)/(4)=(2m^(2)-3)/(6)`
`"or "m^(2)=(9)/(4)`
`"or "m= pm (3)/(2)`
Therefore, the equation of tangents are
`y-(5)/(2)=pm(3)/(2)(x-0)`
`"or "y=(5)/(2)pm(3)/(2)x`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.4|5 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.5|5 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.2|12 Videos

  • HIGHT AND DISTANCE

    CENGAGE ENGLISH|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

Tangents PA and PB are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

Tangents P Aa n dP B are drawn to x^2+y^2=a^2 from the point P(x_1, y_1)dot Then find the equation of the circumcircle of triangle P A Bdot

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1)dot

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1) .

Tangents are drawn to the hyperbola x^(2)-y^(2)=3 which are parallel to the line 2x+y+8=0 . Then their points of contact is/are :

How many real tangents can be drawn from the point (4, 3) to the hyperbola (x^2)/(16)-(y^2)/9=1? Find the equation of these tangents and the angle between them.

Tangents are drawn from (-2,1) to the hyperola 2x^(2)-3y^(2)=6 . Find their equations.

Tangents are drawn from (-2,1) to the hyperola 2x^(2)-3y^(2)=6 . Find their equations.

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

Tangents are drawn to the parabola (x-3)^2+(y-4)^2=((3x-4y-6)^2)/(25) at the extremities of the chord 2x-3y-18=0 . Find the angle between the tangents.