List of top Mathematics Questions on Coordinate Geometry asked in VITEEE

The normal at the point \( (t_1, t_2) \) on the parabola, cuts the parabola again at the point whose parameter is

The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is

The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is

The foci of the ellipse \( \frac{x^2}{144} + \frac{y^2}{81} = 1 \) and the hyperbola \( \frac{x^2}{144} - \frac{y^2}{81} = 1 \) coincide then value of \( b^2 \) is

The equation of tangents to the hyperbola \( 3x^2 - 2y^2 = 6 \) which is perpendicular to the line \( x - 3y = 3 \) is

The area of the region bounded by the curves \( x^2 + y^2 = 9 \) and \( x + y = 3 \) is

The normal at the point \( (a t^2, 2 a t) \) on the parabola meets the parabola again at the point \( (a t^2, 2 a t) \). The equation of the normal is

The given equation of rectangular hyperbola is \[ x^2 - y^2 = 6^2 \quad \text{(length of latus rectum is 16)} \] The asymptotes are parallel to each other

If \( l = x^2 + y^2 + z^2 \) is a normal to the ellipse \[ \frac{x^2}{16} + \frac{y^2}{9} = 1, \] then

If \( \text{line} \, y = mx + c \) is a normal to the ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \] then \( c^2 \) is equal to

The area in the first quadrant between \( x^2 + y^2 = 4 \) and \( y = \sin x \) is?

The area bounded by \( y = x \) and \( lines |x| = 1 \) is?

The angle between lines joining the origin to the point of intersection of the line \( \sqrt{3}x + y = 2 \) and the curve \( y^2 = x^3 \) is?

Two lines \( x - y + 1 = 1 \) and \( x - 3y - k = 2 \) intersect at a point, if \( k \) is equal to?

If a tangent having slope \( \frac{-4}{3} \) to the ellipse \[ \frac{x^2}{18} + \frac{y^2}{32} = 1 \] intersects the major and minor axes in points A and B respectively, then the area of \( \triangle OAB \) is equal to

The locus of mid points of tangents intercepted between the axes of ellipse \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] is

If \( P \) is a double ordinate of hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] such that \( OPQ \) is an equilateral triangle, \( O \) being the centre of the hyperbola, then the eccentricity \( e \) of the hyperbola satisfies

The line joining two points \( A(2,0) \), \( B(3,1) \) is rotated about \( A \) in anti-clockwise direction through an angle of \( 15^\circ \). The equation of the line in the new position is

The line \( 2x + \sqrt{6}y = 2 \) is tangent to the curve \( x^2 - 2y^2 = 4 \). The point of contact is

The number of integral points (integral point means both the coordinates should be integers) exactly in the interior of the triangle with vertices \( (0, 0), (0, 21), (21, 0) \) is

The centres of a set of circles, each of radius 3, lie on the circle \( x^2 + y^2 = 25 \). The locus of any point in the set is

The angle of intersection of the circles \( x^2 + y^2 - 8x - 9 = 0 \) and \( x^2 + y^2 + 2x - 4y - 11 = 0 \) is

The eccentricity of the ellipse, which meets the straight line \( \frac{x}{7} + \frac{y}{2} = 1 \) on the axis of \( x \) and the straight line \( \frac{x}{3} - \frac{y}{5} = 1 \) on the axis of \( y \), and whose axes lie along the axes of coordinates, is:

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

The equation of the conic with focus at \( (1, -1) \), directrix along \( x - y + 1 = 0 \), and eccentricity \( \sqrt{2} \) is: