Ellipse questions
211 published questions with worked solutions.
- In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is
- A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the...
- The ellipse x^2 + 4y^2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another...
- Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity 25...
- The ellipse 4x^2+9y^2=1 intersects positive Y-axis at point A. If S and S' are its foci, then the area (in sq. units) of SAS' is...
- If the line 3x + 4y + k = 0 touches the ellipse 9x^2 + 16y^2 = 144, then the value of k is.
- The equations of the tangents to the ellipse x^2 16 + y^2 9 =1 making an inclination of 30^ with the major axis are
- If the eccentricity of the ellipse x^2 a^2 + y^2 b^2 =1, (a>b) is 2 3 and its focal chord is 3x+2y-6=0, then the value of a^2+b^2...
- The eccentricity of the ellipse 9x^2 + 5y^2 - 30y = 0 is
- An ellipse has OB as semi-minor axis, S and S' are foci and angle SBS' is a right angle. Then the eccentricity of the ellipse is
- The eccentricity of the ellipse represented by the equation 7x^ 2 +16y^ 2 -14x+64y-277=0 is...
- A tangent having slope - 1 2 to the ellipse 3x^2 + 4y^2 = 12 intersects the X-axis and Y-axis at the points A and B respectively....
- The equations of two ellipses are be x^2 4 + y^2 2 =1 and x^2 36 + y^2 b^2 =1. If the product of their eccentricities is 2 3 ,...
- If P be any point on the ellipse 16x^2 + 25y^2 = 400 with foci S and S' and area of PSS' is 9 square units, then the abscissa of...
- If is the eccentric angle of a point on the ellipse x^2 25 + y^2 9 =1 such that the distance of the point from the center is 5,...
- The foci of the conic 25x^2+16y^2-150x=175 are
- The eccentricity of the curve represented by x = 3 (cos t + sin t), y = 4 (cos t – sin t) is
- The tangent to the ellipse 9x^2 + 16y^2 = 288 making equal intercepts on the co-ordinate axes intersects X-axis and Y-axis in the...
- The eccentric angle of the point P(-6,2) of the ellipse x^2 48 + y^2 16 =1 is
- If P_1 and P_2 are two points on the ellipse x^2 4 + y^2 = 1 at which the tangents are parallel to the chord joining the points...
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