List of top Mathematics Questions on Geometry asked in AP EAPCET

If the velocity of a particle moving on a straight line is proportional to the cube root of its displacement, then its acceleration is
The angle between the tangents drawn from point (1, 4) to parabola \(y^2 = 4x\) is
If the equation of the tangent of the hyperbola \( 5x^2 - 9y^2 - 20x - 18y - 34 = 0 \) which makes an angle \( 45^\circ \) with the positive X-axis in positive direction is \( x+by+c=0 \) then \( b^2+c^2 = \)
If the intercepts made by a variable circle on the X-axis and Y-axis are 8 and 6 units respectively, then the locus of the center of the circle is:
If the intercept of a line \(L\) made between the straight lines \(5x - y - 4 = 0\) and \(3x + 4y - 4 = 0\) is bisected at the point (1, 5), then the equation of \(L\) is
If the perpendicular distances from the points \( (2,3) \), \( (4,a) \), and \( (\alpha, \beta) \) onto the line \( 3x + 4y - 3 = 0 \) are equal and \( 4\alpha - 3\beta + 1 = 0 \), then the sum of all possible values of \( \alpha \), \( \alpha \) and \( \beta \) is:
If the chord joining points \((1,2)\) and \((2,-1)\) on a circle subtends an angle \(\frac{\pi}{4}\) at any point on its circumference, then the equation of such a circle is?
If the function \(y = \sin(x)(1 - \cos x)\) is defined in the interval \([-\pi, \pi]\), then y is strictly increasing in the interval
If \(\alpha\) is the angle made by the perpendicular drawn from origin to the line \(12x - 5y + 13 = 0\) with the positive X-axis in anti-clockwise direction, then \(\alpha =\)
The equations of the asymptotes of a hyperbola are \( x+y+3=0 \), \( 2x-y+1=0 \). If \( (1,-2) \) is a point on this hyperbola, then the equation of its conjugate hyperbola is:
A line \(L_1\) passing through the point of intersection of the lines \(x-2y+3=0\) and \(2x-y=0\) is parallel to the Line \(L_2\). If \(L_2\) passes through origin and also through the point of intersection of the lines \(3x-y+2=0\) and \(x-3y-2=0\), then the distance between the lines \(L_1\) and \(L_2\) is
The equation of the base of an equilateral triangle is \( x + y = 2 \) and its opposite vertex is \( (2,1) \). If \( m_1, m_2 \) are the slopes of the other two sides and the length of its side is \( a \), then \( |m_1 - m_2| + a\sqrt{2} = \):
If \((2, -1, 3)\) is the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to a plane then the equation of that plane is
If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
A line \(L\) passes through point \(P(1, 2)\) and makes an angle of \(60^\circ\) with OX in positive direction. A and B are points on line \(L\), 4 units from P. If O is origin, then area of \(\triangle OAB\) is
If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are the tangents to the same circle, then the area of that circle (in sq. units) is
If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle \( \frac{\pi}{4} \) with the negative X-axis in the negative direction, then the equation of that line is
The equation of chord AB of ellipse \(2x^2 + y^2 = 1\) is \(x - y + 1 = 0\). If O is the origin, then \(\angle AOB =\)
If the equation of the plane passing through the point (2, -1, 3) and perpendicular to each of the planes $3x - 2y + z = 8$ and $x + y + z = 6$ is $lx + my + nz = 1$, then $4m + 2n - 3l$ =
Identify the correct option from the following:
P and Q are the ends of a diameter of the circle \( x^2+y^2=a^2(a>\frac{1}{\sqrt{2}}) \). \( s \) and \( t \) are the lengths of the perpendiculars drawn from P and Q onto the line \( x+y=1 \) respectively. When the product \( st \) is maximum, the greater value among \( s, t \) is:
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
If the equation of the tangent of the hyperbola \( 5x^2 - 9y^2 - 20x - 18y - 34 = 0 \) which makes an angle \( 45^\circ \) with the positive X-axis in positive direction is \( x+by+c=0 \) then \( b^2+c^2 = \)
The triangle formed by the lines \( 2x^2 + xy - 6y^2 = 0 \) and \( x+y-1=0 \) is:
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
If two sides of a triangle are represented by \( 3x^2 - 5xy + 2y^2 = 0 \) and its orthocentre is (2,1), then the equation of the third side is