Ellipse questions
211 published questions with worked solutions.
- The line 12x cos + 5y sin = 60 is tangent to which of the following curves ?
- Let an ellipse E: x^2 a^2 + y^2 b^2 =1, a^2>b^2, passes through ( 3 2 ,1 ) and has eccentricity 1 3 . If a circle, centered at...
- On the ellipse x^2 8 + y^2 4 =1 let P be a point in the second quadrant such that the tangent at P to the ellipse is...
- Let L be a common tangent line to the curves 4x^2+9y^2=36 and (2x)^2+(2y)^2=31. Then the square of the slope of the line L...
- Let the maximum area of the triangle that can be inscribed in the ellipse x^ 2 /a^ 2 + y^ 2 /4 = 1, a > 2, having one of its...
- The locus of the point P(x,y) satisfying the relation (x-3)^2+(y-1)^2 + (x+3)^2+(y-1)^2 =6 is
- If the ellipse x^ 2 /a^ 2 + y^ 2 /b^ 2 = 1 meets the line x/7 + y/(2 6 ) = 1 on the x-axis and the line x/7 − y/(2 6 ) = 1 on the...
- The line y = x + 1 meets the ellipse x^ 2 /4 + y^ 2 /2 = 1 at two points P and Q. If r is the radius of the circle with PQ as...
- The acute angle between the pair of tangents drawn to the ellipse 2x^ 2 + 3y^ 2 = 5 from the point (1, 3) is
- The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x^ 2 + 2y^ 2 = 4 is an...
- Let the common tangents to the curves 4(x^ 2 + y^ 2 ) = 9 and y^ 2 = 4x intersect at the point Q. Let an ellipse, centered at the...
- The line x = 8 is the directrix of the ellipse E : x^2 a^2 + y^2 b^2 =1 with the corresponding focus (2, 0). If the tangent to E...
- Let the eccentricity of an ellipse x^2 a^2 + y^2 b^2 =1 is reciprocal to that of the hyperbola 2x^2-2y^2=1. If the ellipse...
- The ellipse E_1 : x^2 9 + y^2 4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another...
- A vertical line passing through the point (h, 0) intersects the ellipse x^2 4 + y^2 3 = 1 at the points P and Q. Let the tangents...
- Let E_1 and E_2 be two ellipses whose centers are at the origin. The major axes of E_1 and E_2 lie along the x-axis and the...
- Consider two straight lines, each of which is tangent to both the circle x^2+y^2= 1 2 and the parabola y^2=4x. Let these lines...
- Define the collections E_1,E_2,E_3, of ellipses and R_1,R_2,R_3, of rectangles as follows: E_1: x^2 9 + y^2 4 =1; R_1: rectangle...
- The locus of a point such that the sum of its distances from the points (0, 2) and (0, -2) is 6, is
- The curve represented by x = 3( t + t), y = 4( t - t) is
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