﻿ An ellipse has eccentricity  and one focus at the point . Its one directrix is the common tangent nearer to the point P, to the circle x2 + y2 = 1 and the hyperbola x2 – y2 =1. The equation of the ellipse in the standard from is : Kaysons Education

# An Ellipse Has Eccentricity  and One Focus At The Point . Its One Directrix Is The Common Tangent Nearer To The Point P, To The Circle x2 + y2 = 1 And The Hyperbola x2 – y2 =1. The Equation Of The Ellipse In The Standard From Is

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## Question

### Solution

Correct option is

There are two common tangents namely x = 1, x = –1 to the

xy2 = 1 and hyperbola x2 – y2 =1. Out of these only x – 1= 0 is nearer to point . Which is focus of the required ellipse. According to the given condition x – 1 = 0   … (1), is directrix of the ellipse. If Q(x, y) is any point of ellipse, then by def. of ellipse .

distance of G from (1).

Simplify to get

#### SIMILAR QUESTIONS

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