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

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

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   

                          

Testing

SIMILAR QUESTIONS

Q1

The locus of the poles of normal chords of an ellipse is given by

Q2

Let be the perpendicular distance from the center of the ellipse  to the tangent drawn at point P on the ellipse. If F1and F2 are the two foci of the ellipse, then. Where k =

Q3

The maximum area of an isosceles triangle inscribed in the ellipse  with its vertex at one end of the major axis is

Q4

The eccentricity of the curve x2 + 2y2 – 2x + 3+ 2 = 0 is

Q5

A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Then angle between the tangents at P and Q of the ellipse  x2 + 2y2 = 6 is

Q6

Tangents are drawn to the ellipse  at the end of latus rectum. Find the area of quadrilateral so formed   

Q7

The eccentricity of the ellipse which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lies along the axes of coordinates is

Q8

The line lx + my + n = 0 is a normal to the ellipse  if

Q9

If the normal at any point P on the ellipse cuts the major and minor axes in G and g respectively and C be the center of the ellipse

Q10

The angle between the pair of tangents drawn from the point (1, 2) to the ellipse 3x2 + 2y2 = 5 is