List of top Mathematics Questions on Coordinate Geometry

Let A₁, B₁, C₁ be three points in the xy -plane. Suppose that the lines A₁C₁ and B₁C₁ are tangents to the curve y² = 8x at A₁ and B₁, respectively. If O = (0,0) and C₁ = −( 4, 0), then which of the following statements is (are) TRUE ?

Let \(S=\left\{(x,y)\in\R\times\R:x\ge0,y\ge0,y^2\le12-2x\ \text{and}\ 3y+\sqrt8\ x\le5\sqrt8\right\}\). If the area of the region S is \(\alpha\sqrt2\), then α is equal to

Let the straight line y = 2x touch a circle with center (0, α), α > 0, and radius r at a point A₁. Let B₁ be the point on the circle such that the line segment A₁B₁ is a diameter of the circle. Let \(α+r=5+\sqrt5\).
Match each entry in List-I to the correct entry in List-II.

List - I		List - II
(P)	α equals	(1)	(-2, 4)
(Q)	r equals	(2)	\(\sqrt5\)
(R)	A1 equals	(3)	(-2, 6)
(S)	B1 equals	(4)	5
		(5)	(2, 4)

The correct option is

If a curve passes through the point (1, 1) at any point (x, y) on the curve, the product of the slope of its tangent and x co-ordinate of the point is equal to the y co-ordinate of the point, then the curve also passes through the point

The area of a triangle with vertices(-3,0),(3, 0) and (0, k) is 9 sq.units, the value of k is

A triangle is formed by the tangents at the point \((2,2)\) on the curves \(𝑦^2=2𝑥\) and \(𝑥^2+𝑦^2=4𝑥\), and the line \(𝑥+𝑦+2=0\). If \(𝑟\) is the radius of its circumcircle, then \(𝑟^2\) is equal to ____ .

Let (α, β) be the centroid of the triangle formed by the lines 15x – y = 82, 6x – 5y = – 4 and 9x + 4y = 17. Then α + 2β and 2α − β are the roots of the equation

The distance of the origin from the centroid of the triangle whose two sides have the equations
x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :

A point P moves so that the sum of squares of its distances from the points (1, 2) and (–2, 1) is 14. Let f(x, y) = 0 be the locus of P, which intersects the x-axis at the points A, B and the y-axis at the points C, D. Then the area of the quadrilateral ACBD is equal to

The corner points of the feasible region of an LPP are (0,2), (3,0), (6,0), (6,8) and (0,5), then the minimum value of z = 4x + 6y occurs at

A dietician has to develop a special diets using two foods X and Y. Each packet (containing 30g) of food. X contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Y contains 3units of calcium , 20 unit of iron, 4 units of cholesterol and 3 units of vitamin A.The diet requires atleast 240 units of calcium, atleast 460 units of iron and atmost 300 units of cholesterol. The corner points of the feasible region are

Consider a triangle \(Δ\) whose two sides lie on the x-axis and the line \(x + y + 1 = 0\). If the orthocenter of \(Δ\) is (1, 1), then the equation of the circle passing through the vertices of the triangle \(Δ\) is;

The mid points of the sides of triangle are (1, 5, -1) (0, 4, -2) and (2, 3, 4) then centroid of the triangle

The equation of straight line which passes through the point (a cos³θ, a sin³θ) and perpendicular to x secθ+y cosecθ = a is

If a plane meets the coordinate axes at A, B and C in such a way that the centroid of triangle ABC is at the point (1, 2, 3) then the equation of the plane is

Let $L_{1}$ and $L_{2}$ be the following straight lines
$L_{1}: \frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{3}$ and $L_{2}: \frac{x-1}{-3}-\frac{y}{-1}=\frac{z-1}{1} $
Suppose thestraight line
$L: \frac{x-\alpha}{1}=\frac{y-1}{m}=\frac{z-\gamma}{-2}$
lies in the plane containing $L_{1}$ and $L_{2}$, and passes through thepoint of intersection of $L_{1}$ and $L_{2}$. If the line $L$ bisects the acute angle between the lines $L_{1}$ and $L_{2}$, then which of the following statements is/are TRUE?

If the curves 2x = y² and 2xy = K intersect perpendicularly, then the value of K² is

The two lines lx + my = n and l'x + m'y = n' are perpendicular if