List of top Mathematics Questions on Coordinate Geometry asked in AP EAMCET

The orthocentre of triangle formed by points: \( (2,1,5) \), \( (3,2,3) \) and \( (4,0,4) \) is:
If the line through the point \( P(5,3) \) meets the circle \( x^2 + y^2 - 2x - 4y + \alpha = 0 \) at \( A(4, 2) \) and \( B(x_1, y_1) \), then \( PA \times PB = \):
If \( (\alpha, \beta, \gamma) \) are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then \( (\alpha + \beta + \gamma)^2 \) is:
The angle subtended by the chord \( x + y - 1 = 0 \) of the circle \( x^2 + y^2 - 2x + 4y + 4 = 0 \) at the origin is: 
If the circles \( x^2 + y^2 + 2ax + 2y - 8 = 0 \) and \( x^2 + y^2 - 2x + ay - 14 = 0 \) intersect orthogonally, then the distance between their centers is:
Find the equation of a line passing through the intersection of \( 3x + y - 4 = 0 \) and \( x - y = 0 \), and making a \( 45^\circ \) angle with \( x - 3y + 5 = 0 \).
If \( Q(h, k) \) is the inverse point of \( P(1,2) \) with respect to the circle \( x^2 + y^2 - 4x + 1 = 0 \), then \( 2h + k \) is:
The triangle \( PQR \) is inscribed in the circle \[ x^2 + y^2 = 25. \] If \( Q = (3,4) \) and \( R = (-4,3) \), then \( \angle QPR \) is:
If \( A(1,2,0), B(2,0,1), C(-3,0,2) \) are the vertices of \( \triangle ABC \), then the length of the internal bisector of \( \angle BAC \) is:
The origin is shifted to the point \( (2, 3) \) by translation of axes and then the coordinate axes are rotated about the origin through an angle \( \theta \) in the counter-clockwise sense. Due to this if the equation \( 3x^2 + 2xy + 3y^2 - 18x - 22y + 50 = 0 \) is transformed to \( 4x^2 + 2y^2 - 1 = 0 \), then the angle \( \theta = \):
The equation of a line which makes an angle of \( 45^\circ \) with each of the pair of lines \[ xy - x - y + 1 = 0 \] is:
The equation of the locus of points that are equidistant from the points \( (2,3) \) and \( (4,5) \) is:
The transformed equation of \( x^2 - y^2 + 2x + 4y = 0 \) when the origin is shifted to the point \( (-1,2) \) is:
The equation of one side of an equilateral triangle is \( x + y = 2 \), and one vertex is \( (2,-1) \). The length of the side is:
If the perpendicular distance from \( (1,2,4) \) to the plane \( 2x + 2y - z + k = 0 \) is 3, then \( k \) is:
The length of the tangent drawn from the point \( \left(\frac{k}{4}, \frac{k}{3}\right) \) to the circle \( x^2 + y^2 + 8x - 6y - 24 = 0 \) is:
If \( (a, b) \) is the stationary point of the curve \( y = 2x - x^2 \), then the area bounded by the curves \( y = 2x - x^2 \), \( y = x^2 - 2x \), and \( x = a \) is:

The circle S = x2 + y2 − 2x − 4y + 1 = 0 cuts the y-axis at A, B (OA: OB). If the radical axis of S ≡ 0 and S′ = x2 + y2 − 4x − 2y + 4 = 0 cuts the y-axis at C, then the ratio in which C divides AB is:

Suppose the axes are to be rotated through an angle \( \theta \) so as to remove the \( xy \) term from the equation \(3 x^2 + 2\sqrt{3}xy + y^2 = 0 \). Then in the new coordinate system, the equation \( x^2 + y^2 + 2xy = 2 \) is transformed to:
A ray of light passing through the point (2, 3) reflects on the Y-axis at a point P. If the reflected ray passes through the point (3, 2) and P = (a, b), then 5b = ?

Let P be any point on the circle x2 + y2 = 25. Let L be the chord of contact of P with respect to the circle x^2 + y^2 = 9. The locus of the poles of the lines L with respect to the circle x2 + y2 = 36 is:

The locus of a variable point which forms a triangle of fixed area with two fixed points is:
If the axes are rotated through an angle \( \alpha \), then the number of values of \( \alpha \) such that the transformed equation of \( x^2 + y^2 + 2x + 2y - 5 = 0 \) contains no linear terms is:
If a man of height 1.8 m is walking away from the foot of a light pole of height 6 m with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph):
If the equation \( \frac{x^2}{7-k} - \frac{y^2}{5-k} = 1 \) represents a hyperbola, then: