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let A(x1,0) and B(x2,0) be the foci of t...

let `A(x_1,0)` and `B(x_2,0)` be the foci of the hyperbola `x^2/9-y^2/16=1` suppose parabola having vertex at origin and focus at `B` intersect the hyperbola at `P` in first quadrant and at point Q in fourth quadrant.

A

`(-(9)/(10),0)`

B

`((2)/(3),0)`

C

`((9)/(10),0)`

D

`((2)/(3),sqrt(6))`

Text Solution

Verified by Experts

`a=3,e=(1)/(3)`
`:. F_(1)-=(-1,0) and F_(2)-=(1,0)`
SO, equation of parbola is `y^(2)=4x`

Solving ellipse and parabola, we get points of intersection as
`M((3)/(2),sqrt(6)) 1 and M((3)/(2),sqrt(6))`
Orthocentre of `DeltaF_(1)`MN lioes onb x-axis.
Slope of `F_(1)N=(-sqrt(6)-0)/((3)/(2)+1)=(-2sqrt(6))/(5)`
Putting y=0 or orhtocentre, we get `y=-(9)/(10)`
So, orthocenter is `(-(9)/(10),0)`
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