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Tangents are drawn to the parabola (x-3)...

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.

A

A. `90^o`

B

B. `45^o`

C

C. `60^o`

D

D. `30^o`

Text Solution

Verified by Experts

We have equation of parabola,
`sqrt((x-3)^(2)+(y+4)^(2))=(|3x-4y-6|)/(sqrt(3^(2)+(-4)^(2)))`
Focus of the parabola is (3,-4) and directrix is 3x-4y-6=0. The given chord 2x-3y-18=0 passes through the focus (3,-4) of the parabola. So, it is focal chord.
Since tangents drawn at the extremities of focal chord are perpendicular, angle between tangents is `90^(@)`.
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Knowledge Check

  • From the point (-1, -6) two tangents are drawn to the parabola y^(2)= 4x . Then the angle between the tangents is-

    A
    ` 30 ^(@)`
    B
    ` 45 ^(@)`
    C
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    D
    ` 60 ^(@)`

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