List of top Mathematics Questions

Find the length of the intercept made by the line $ x + 1 = 0 $ between the lines: $$ 3x + 2y = 5 \quad \text{and} \quad 3x + 2y = 3 $$
Let the slopes $ m_1 $ and $ m_2 $ of the lines represented by: $$ ax^2 + 2hxy + by^2 = 0 $$ satisfy: $$ 3(m_1 - m_2) - 7 = 0 \quad \text{and} \quad m_1 m_2 - 2 = 0 $$ Then find the correct relation among $ a, b, h $.
The locus of the point of intersection on the line \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) and \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) for different real values of k is a hyperbola H. If e is the eccentricity of H then \(4e^2 = \)
On the locus of the point \( P(x, y) \) equidistant from \( (3, 0) \) and \( (0, 4) \), if \( A \) and \( B \) are two points that satisfy \( 4x = 3y \) and \( x = y \) respectively, then the distance between A and B is:
A circle has its centre in the first quadrant and passes through $(2, 3)$. If this circle makes intercepts of length 3 and 4 respectively on $x = 2$ and $y = 3$, its equation is
The straight line touching the circle \(x^2+y^2-2x-3=0\) and remaining normal to the circle \(x^2+y^2-4y-6=0\) is
The equation of circle with centre (2, -3) and touching x-axis is
The straight line passing through \( (0, 0) \) and the foot of the perpendicular from \( (2, 4) \) onto the line \( x + y - 1 = 0 \) is:
Three points $ A, B, C $ in the plane have: - x-coordinates in G.P. - y-coordinates in the same G.P. Then, the points $ A, B, C $ lie on:
Two distinct points are each at a unit distance from the line \( 4x + 3y - 10 = 0 \) and lie on the line \( x + y = 4 \). If they are separated by distance \( d \), then:
If \( ax^2 - 34xy - 5y^2 + 2x + 26y - 5 = 0 \) represents a pair of straight lines, then the value of a is
Suppose \( d_1 \) and \( d_2 \) are respectively the lengths of intercepts of the circle \( x^2 + y^2 = 4 \) and \( x^2 + y^2 - 10x - 14y + 65 = 0 \) on the line \( 2x - 2y = 3 \). Then which of the following is true?
The image of the point $(3, 4)$ with respect to the radical axis of the circles $x^2 + y^2 + 8x + 2y + 10 = 0$ and $x^2 + y^2 + 7x + 3y + 10 = 0$ is
Find the least distance from the point $ (10, 7) $ to the circle: $$ x^2 + y^2 - 4x - 2y - 20 = 0 $$
The ratio of the areas of the greatest and the smallest circles touching \((x \pm 1)^2 + (y \pm 1)^2 = 1\) is (The equation \((x \pm 1)^2 + (y \pm 1)^2 = 1\) represents four circles with radius 1, centered at (1,1), (1,-1), (-1,1), (-1,-1).)
Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?
Suppose a triangle is formed by $x + y = 10$ and the coordinate axes. Then the number of points $(x, y)$ where $x$ and $y$ are natural numbers, lying inside the triangle is
The locus of centers of the circles, possessing the same area and having $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as their common tangent, is
Starting from the point $A(-3,4)$, a moving object touches $2x + y - 7 = 0$ at $B$ and reaches $C(0,1)$. If the object travels along the shortest path, the distance between $A$ and $B$ is
Let point $ P $ divide the line segment joining $ A(1, 2, -1) $ and $ B(-1, 0, 1) $ externally in the ratio $ 1:2 $. Given point $ Q = (1, 3, -1) $, find $ PQ $.
Let the coordinates of points A and B satisfy:
- $ x^2 + 2x - a^2 = 0 $
- $ y^2 + 4y - b^2 = 0 $ Find the equation of the circle having AB as diameter.
The pole of the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is
Find the set of all points at a distance of at least 2 units from the point \( (-3, 0) \).
In a square ABCD of side length a, suppose AB and AD are along the coordinate axes. Then the circle that circumscribes the square is
The equation of the circle passing through the origin and cutting orthogonally the circles \( x^2 + y^2 + 6x - 15 = 0 \) and \( x^2 + y^2 - 8y - 10 = 0 \) is: