List of top Mathematics Questions on Geometry asked in AP EAPCET

Let \( a, b, c, d \) be non-zero numbers. If the point of intersection of the lines \( 4ax + 2ay + c = 0 \) and \( 5bx + 2by + d = 0 \) lies in the fourth quadrant and is equidistant from the two coordinate axes, then the relationship between \( a, b, c, d \) is:
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the positive X-axis and positive Y-axis respectively, then the angle made by \( L \) with the positive direction of the Z-axis is:
Let \( C \) be the centre and \( A \) be one end of a diameter of the circle \( x^2 + y^2 - 2x - 4y - 20 = 0 \). If \( P \) is a point on \( AC \) such that \( CP : PA = 2 : 3 \), then the locus of \( P \) is:
If \( P \left( \frac{\pi}{3} \right) \) and \( Q \left( \frac{2\pi}{3} \right) \) represent two points on the circle \( x^2 + y^2 - 4x - 6y - 12 = 0 \) in parametric form, then the length of the chord PQ is:
A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular drawn from the origin to this line makes an angle of 60° with the line \( x + y = 0 \). Then the equation of the line L is:
The equation of a plane passing through \( (-1, 2, 3) \) and whose normal makes equal angles with the coordinate axes is:
If the angle between the pair of lines \( x^2 + 2\sqrt{2} xy + ky^2 = 0, k>0 \) is \( 45^\circ \), then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line \( x + 2y + 1 = 0 \) is
The coordinates of the point \( (3, -5) \) in the new system, when the origin is shifted to the point \( (-1, -1) \) by the translation of axes, is
The absolute value of the tangent of the difference of the angles made by the lines \( 4x^2 - 24xy + 11y^2 = 0 \) with the X-axis is:
In $ \triangle ABC $, the expression $ \frac{a}{s-a} + \frac{b}{s-b} + \frac{c}{s-c} $ is equivalent to:
A point on the straight line \( 3x + 5y = 15 \) which is equidistant from the coordinate axes will lie in
An equation of a plane parallel to the plane \( x - 2y + 2z - 5 = 0 \) and which is at one unit distance from the origin is:
Given that the solid obtained by rotating a rectangle about one of its sides is a cylinder. If the perimeter of a rectangle is 48 cm and the volume of the cylinder formed by rotating it is maximum, then the dimensions of that rectangle is
Let \( P(h, k) \) be the point of contact of the tangent to the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) which is parallel to the line \( \sqrt{3}x - y + 1 = 0 \). If \( P \) lies in the fourth quadrant then \( 3h^2 - 2k = \)
If \( f(x) = px^3 + qx^2 + rx + t \) attains local minimum and local maximum values at \( x = -2 \) and \( x = 2 \) respectively and \( p \) is a root of \( 9x^2 - 1 = 0 \), then \( p + q + r = \)
Let the length of the latus rectum of an ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) be equal to the length of its semi-major axis. If the radius of its director circle is \( \sqrt{3} \) and \( e \) is its eccentricity, then the length of its latus rectum is:
If \( A(4, 0) \) and \( B(-4, 0) \) are two points, then the locus of a point \( P \) such that \( PA - PB = 4 \) is:
The lines \( p(x^2 + 1) + x - y + q = 0 \) and \( (p^2 + 1)x^2 + (p^2 + 1)y + 2q = 0 \) are perpendicular to a line L. Then the equation of the line L is:
If \( 2x^2 - 3xy + y^2 = 0 \) represents two sides of a triangle and \( x + y - 1 = 0 \) is its third side, then the distance between the orthocenter and the circumcenter of that triangle is:
If \( S \) is the set of all real values of \( a \) such that a plane passing through the points \( (-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2) \) also passes through the point \( (-1, -1, 1) \), then \( S = \dots \)
The distance between the centres of similitude of the circles \( x^2 + y^2 + 6x - 8y + 16 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is:
Let P and Q be the inverse points with respect to the circle \( S = x^2 + y^2 - 4x - 6y + k = 0 \), and C be the center of the circle. If \( CP.CQ = 4 \), and \( P = (1, 2) \), then \( Q = (a, b) \) and \( 2a = \dots \)
The perpendicular distance from the origin to the focal chord drawn through the point \( (4, 5) \) to the parabola \( y^2 - 4y - 3x + 7 = 0 \) is:
If the angle between the curves \( y = e^{(x+4)} \) and \( x^2 y = 1 \) at the point \( (1, 1) \) is \( \theta \), then \[ \sin \theta + \cos \theta = \dots \]
If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12, then the equation of that line which forms a triangle of maximum area with the coordinate axes is: