List of top Mathematics Questions on Coordinate Geometry asked in NIT MCA Common Entrance Test

The circle $ x^2 + y^2 + ax + by + \gamma = 0 $ is the image of the circle $ x^2 + y^2 - 6x - 10y + 30 = 0 $ across the line $ 3x + y = 2 $. The value of $ [\alpha + \beta + \gamma] $ is (where $ [.] $ represents the floor function)

An equilateral triangle is inscribed in the parabola $ y^2 = x $. One vertex of the triangle is at the vertex of the parabola. The centroid of the triangle is:

A circle with its center in the first quadrant touches both the coordinate axes and the line $ x - y - 2 = 0 $. Then the area of the circle is:

Let the line $\frac{x}{4} + \frac{y}{2} = 1$ meet the x-axis and y-axis at A and B, respectively. M is the midpoint of side AB, and M' is the image of the point M across the line $x + y = 1$. Let the point P lie on the line $x + y = 1$ such that $\Delta ABP$ is an isosceles triangle with $AP = BP$. Then the distance between M' and P is:

Let $ F_1, F_2 $ $\text{ be the foci of the hyperbola}$ \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, a > 0, \, b > 0, \] and let $ O $ be the origin. Let $ M $ be an arbitrary point on curve $ C $ and above the X-axis and $ H $ be a point on $ MF_1 $ such that $ MF_2 \perp F_1 F_2, \, M F_1 \perp OH, \, |OH| = \lambda |O F_2| $ with $ \lambda \in (2/5, 3/5) $, then the range of the eccentricity $ e $ is in:

The equation of the circle passing through the point $ (1, 2) $ and touching both axes is:

The locus of the mid-point of all chords of the parabola $ y^2 = 4x $ which are drawn through its vertex is:

Let $ a, b, c, d $ be non-zero numbers. If the point of intersection of the lines \[ 4ax + 2ay + c = 0 \text{and} 5bx + 2by + d = 0 \] lies in the fourth quadrant and is equidistant from the two, then the relation between $ a, b, c, d $ is

The range of values of $ \theta $ in the interval $ \left( 0, \pi \right) $ such that the points $ (3, 2) $ and $ (\cos \theta, \sin \theta) $ lie on the same sides of the line $ x + y - 1 = 0 $, is:

Find foci of the equation $ x^2 + 2x - 4y^2 + 8y - 7 = 0 $

A point $ P $ in the first quadrant, lies on $ y^2 = 4ax $, $ a > 0 $, and keeps a distance of $ 5a $ units from its focus. Which of the following points lies on the locus of $ P $?

A circle touches the x-axis and also touches the circle with centre (0, 3) and radius 2. The locus of the centre of the circle is

If the foci of the ellipse $ \frac{x^2}{25} + \frac{y^2}{b^2} = 1 $ and the hyperbola $ \frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25} $ are coincide, then the value of $ b^2 $ is

Let a be the distance between the lines $ -2x + y = 2 $ and $ 2x - y = 2 $, and b be the distance between the lines $ 4x - 3y = 5 $ and $ 6y - 8x = 1 $, then

Coordinate of focus of the parabola $4y^2 + 12x - 20y + 67 = 0$ is

If $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ ($ a > b $) and $ x^2 - y^2 = c^2 $ cut at right angles, then

A straight line through the point (4, 5) is such that its intercept between the axes is bisected at A, then its equation is