Ellipse questions
211 published questions with worked solutions.
- If the line x + 4y = 7 , where R, touches the ellipse 3x^2 + 4y^2 = 1 at the point P in the first quadrant, then one of the focal...
- Let S and S' be the foci of the ellipse x^2 25 + y^2 9 =1 and P( , ) be a point on the ellipse in the first quadrant. If...
- Let the line y-x=1 intersect the ellipse x^2 2 + y^2 1 =1 at the points A and B. Then the angle made by the line segment AB at...
- Let each of the two ellipses E_1: x^2 a^2 + y^2 b^2 =1, (a>b) and E_2: x^2 A^2 + y^2 B^2 =1, (A<B) have eccentricity 4 5 . Let...
- Let the length of the latus rectum of an ellipse x^2 a^2 + y^2 b^2 =1, (a>b), be 30 . If its eccentricity is the maximum value of...
- Let (h,k) lie on the circle C: x^2+y^2=4 and the point (2h+1, 3k+2) lie on an ellipse with eccentricity e. Then the value of 5...
- An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at (5,-2). Then the length of its latus rectum is :
- The length of the chord of the ellipse x^2 4 + y^2 2 = 1, whose mid-point is (1, 1 2 ), is :
- Let the product of the focal distances of the point ( 3 , 1 2 ) on the ellipse x^2 a^2 + y^2 b^2 = 1, (a > b), be 7 4 . Then the...
- The equation of the chord, of the ellipse x^2 25 + y^2 16 =1, whose mid-point is (3,1) is :
- Let E_1 : x^2 9 + y^2 4 = 1 be an ellipse. Ellipses E_i's are constructed such that their centres and eccentricities are same as...
- If x + y = 109 is the equation of the chord of the ellipse x^2 9 + y^2 4 =1, whose mid point is ( 5 2 , 1 2 ) then + is equal to
- If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of...
- If S and S′ are the foci of the ellipse x^2 18 + y^2 9 =1 and P be a point on the ellipse, then min.(SP·S′P) + max.(SP·S′P) is...
- Let C be the circle of minimum area enclosing the ellipse E : x^2 a^2 + y^2 b^2 = 1 with eccentricity 1 2 and foci( 2, 0). Let...
- A line passing through the point P( 5, 5) intersects the ellipse x^2 36 + y^2 25 = 1 at A and B such that (PA).(PB) is maximum....
- Find the length of latus rectum of an ellipse, whose foci are (2, 5) and (2, –3) and the eccentricity of the ellipse is 4 5
- Let the ellipse 3x^2 + py^2 = 4 pass through the centre C of the circle x^2 + y^2 - 2x - 4y - 11 = 0 of radius r. Let f_1, f_2 be...
- The centre of a circle C is at the centre of the ellipse E : x^2 a^2 + y^2 b^2 = 1, a > b. Let C pass through the foci F_1 and...
- Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the...
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