The is a point P on the hyperbola `(x^(2))/(16)-(y^(2))/(6)=1` such that its distance from the right directrix is the average of its distance from the

Question

The is a point P on the hyperbola `(x^(2))/(16)-(y^(2))/(6)=1` such that its distance from the right directrix is the average of its distance from the

The is a point P on the hyperbola `(x^(2))/(16)-(y^(2))/(6)=1` such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is
A. `-64//5`
B. `-32//9`
C. `-64//9`
D. none of these

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
Let `P-=(x,y)`
`therefore" "(a)/(e)+x=((ex-a)+(ex+a))/(2)`
`therefore" "(a)/(e)+x=ex`
`therefore" "(16)/(5)+x=(5)/(4)x`
`x=(64)/(5)`
But, point P lies on the left branch.
Therefore, x-coordinate of P is `(-64)/(5)`.

7 views Answered 2023-02-05 15:29