List of top Mathematics Questions on Geometry asked in AP EAPCET

A circle passing through the point (1,0) makes an intercept of length 4 units on X-axis and an intercept of length \(2\sqrt{11}\) units on Y-axis. If the centre of the circle lies in the fourth quadrant, then the radius of the circle is
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
The radius of the circle passing through the points of intersection of the circles \( x^2+y^2+2x+4y+1=0 \), \( x^2+y^2-2x-4y-4=0 \), and intersecting the circle \( x^2+y^2=6 \) orthogonally is:
If the surface area of a spherical bubble is increasing at the rate of 4 sq.cm/sec, then the rate of change in its volume (in cubic cm/sec) when its radius is 8 cms is
If the direction ratios of two lines \(L_1\) and \(L_2\) are \((1,-2,2)\) and \((-2,3,-6)\) respectively, then the direction ratios of the line which is perpendicular to both \(L_1\) and \(L_2\) are?
G(1,0) is the centroid of the triangle ABC. If A = (1, -4, 2) and B = (3, 1, 0), then AG$^2$ + CG$^2$ =
Identify the correct option from the following:
If the volume of a sphere is increasing at the rate of 12 \( \text{cm}^3/\text{sec} \), then the rate (in \( \text{cm}^2/\text{sec} \)) at which its surface area is increasing when the diameter of the sphere is 12 cm is:
If a hyperbola has asymptotes \(3x-4y-1=0\) and \(4x-3y-6=0\), then the transverse and conjugate axes of that hyperbola are
If the product of the lengths of the perpendiculars drawn from the ends of a diameter of the circle \( x^2 + y^2 = 4 \) onto the line \( x + y + 1 = 0 \) is maximum, then the two ends of that diameter are:
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
If \( \theta \) is the angle between the tangents drawn from the point \( (-1, -1) \) to the circle \( x^2+y^2-4x-6y+c=0 \) and \( \cos\theta = -\frac{7}{25} \), then the radius of the circle is:
If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
The difference between the absolute maximum and absolute minimum values of the function \( f(x) = 2x^3 - 15x^2 + 36x - 30 \) on \( [-1, 4] \) is:
Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) be such that \( x = 0 \) is the only real root of \( P'(x) = 0 \). If \( P(-1)<P(1) \), then in the interval \( [-1,1] \):
The angle made by a line \(L\) with positive X-axis measured in the positive direction is \(\frac{\pi}{6}\) and the intercept made by \(L\) on Y-axis is negative. If \(L\) is at a distance 5 units from the origin, then the perpendicular distance from the point \(\left(1,-\sqrt{3}\right)\) to the line \(L\) is?
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
The equation of the circle touching the lines \(|x-2| + |y-3| = 4\) is?
Let \( A_1 \) be the area of the given ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). Let \( A_2 \) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point P on the given ellipse, then \( A_1 : A_2 = \)
The angle between the tangents drawn from the point (2, 2) to the circle \(x^2 + y^2 + 4x + 4y + c = 0\) is \(\cos^{-1} \left( \frac{7}{16} \right)\). If two such circles exist, then the sum of values of \(c\) is
If \( \left(\frac{1}{10}, \frac{-1}{5}\right) \) is the inverse point of a point (-1, 2) with respect to the circle \( x^2+y^2-2x+4y+c=0 \) then c =
If the equation of the circle lying in the first quadrant, touching both the coordinate axes and the line \( \frac{x}{3} + \frac{y}{4} = 1 \) is \( (x-c)^2+(y-c)^2=c^2 \), then c =
A circle touches the line \(2x + y - 10 = 0\) at (3, 4) and passes through the point (1, -2). Then a point that lies on the circle is
If the function \(f(x) = x^3 + b x^2 + c x - 6\) satisfies all conditions of Rolle's theorem in \([1,3]\) and \[ f'\left(\frac{2\sqrt{3} + 1}{\sqrt{3}}\right) = 0, \] then find \(bc\).
The equation of the circle which cuts all the three circles \[ 4(x-1)^2 + 4(y-1)^2 = 1,
4(x+1)^2 + 4(y-1)^2 = 1,
4(x+1)^2 + 4(y+1)^2 = 1, \] orthogonally is?
On a line with direction cosines l, m, n, \( A(x_1, y_1, z_1) \) is a fixed point. If \( B=(x_1+4kl, y_1+4km, z_1+4kn) \) and \( C=(x_1+kl, y_1+km, z_1+kn) \) (\(k>0\)) then the ratio in which the point B divides the line segment joining A and C is