defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Parabola, Ellipse and Hyperbola Tangents and Normals to Conics
An ellipse has eccentricity \(\frac{1}{2}\) and one focus at the point P\(\left(\frac{1}{2}, 1\right)\). Its one directrix is common tangent to the circle x2 + y2 = 1 and the hyperbola x2 – y2 = 1, nearer to P. Find the equation of the ellipse.
1
\(9\left(x-\frac{1}{3}\right)^2+12(y-1)^2=1\)
2
\(9\left(x-\frac{1}{3}\right)^2-12(y-1)^2=1\)
3
\(9\left(x-\frac{1}{3}\right)^2+8(y-1)^2=1\)
4
\(12\left(x-\frac{1}{3}\right)^2+9(y-1)^2=1\)