List of top Statistical Science Questions on Coordinate Geometry asked in ICAR AIEEA (PG)

In hyperbola, the length of the transverse axis is the distance between:

The center of the circle \(4x^2 + 4y^2 - 8x + 12y - 25 = 0\) is:

The length of the latus rectum of \(x^2 = -9y\) is equal to:

Roots of the equation \(x^3 - 23x^2 + 142x - 120 = 0\) are

The sum and product of the roots of the polynomial \(x^2 - 2x - 8\) are respectively

From point Q which is outside the circle, the length of the tangent to the circle is 24 cm and the distance of Q from the centre is 25 cm, then the radius of the circle is given by

The eccentricity of the parabola is :

Let \(x^2 = -\frac{25}{2}y\) be the equation of a parabola, then the equation of its directrix is given by :

Let $f(x) = \begin{cases} 2^{1/x}, & x \neq 0 \\ 0, & x = 0 \end{cases}$ Then,

Expansion of $f(x) = \log (1+x)$ by Taylor series is :

The derivative of $f(x) = x^{\sin x}$ is}

The equations of asymptotes for the hyperbola \(xy - 3x - 2y = 0\) are:

Equations of the circle circumscribing the triangle formed by the lines \(x + y = 6\), \(2x + y = 4\), \(x + 2y = 5\) is:

For the parabola \(4(y - 1)^2 = -7(x - 3)\), the coordinates of vertex, focus and length of the latus rectum are respectively:

If the angle between the lines joining the foci of an ellipse to an extremity of the minor axis is \(90^\circ\), and the major axis is \(2\sqrt{2}\), then the equation of ellipse and its eccentricity is:

Vertical and horizontal asymptotes of the curve \(y = \frac{3x + 5}{7 - x}\) are respectively:

The center and radius of the circle \(r^2 = 4r \cos \theta\) are: