JEE Advanced · Mathematics

Coordinate geometry

28 practice questions, each with the answer and an explanation.

Practise Coordinate geometry now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 28 questions

What is the distance of the point $(4, 1)$ from the line $6 x + 8 y - 20 = 0$ ?
What is the distance of the point $(3, 4)$ from the line $5 x + 12 y + 9 = 0$ ?
What is the distance of the point $(5, 5)$ from the line $5 x + 12 y + 16 = 0$ ?
What is the distance of the point $(3, 0)$ from the line $3 x + 4 y + 12 = 0$ ?
What is the distance of the point $(6, - 3)$ from the line $5 x + 12 y + 16 = 0$ ?
What is the distance of the point $(- 2, 5)$ from the line $5 x + 12 y + 7 = 0$ ?
What is the distance of the point $(- 3, - 3)$ from the line $6 x + 8 y - 7 = 0$ ?
What is the distance of the point $(3, 0)$ from the line $5 x + 12 y + 7 = 0$ ?
What is the distance of the point $(- 2, 1)$ from the line $8 x + 15 y - 3 = 0$ ?
What is the distance of the point $(- 3, - 2)$ from the line $3 x + 4 y - 7 = 0$ ?
What is the distance of the point $(0, - 2)$ from the line $3 x + 4 y + 14 = 0$ ?
What is the distance of the point $(- 2, 2)$ from the line $5 x + 12 y - 1 = 0$ ?
What is the distance of the point $(6, 2)$ from the line $5 x + 12 y + 10 = 0$ ?
What is the distance of the point $(4, - 1)$ from the line $6 x + 8 y + 11 = 0$ ?
What is the distance of the point $(5, 0)$ from the line $6 x + 8 y + 14 = 0$ ?
What is the distance of the point $(- 1, 6)$ from the line $3 x + 4 y - 13 = 0$ ?
What is the distance of the point $(3, 2)$ from the line $3 x + 4 y - 16 = 0$ ?
What is the distance of the point $(3, 6)$ from the line $8 x + 15 y - 2 = 0$ ?
What is the distance of the point $(2, 1)$ from the line $6 x + 8 y + 4 = 0$ ?
What is the distance of the point $(6, - 2)$ from the line $8 x + 15 y - 14 = 0$ ?
What is the distance of the point $(4, 3)$ from the line $6 x + 8 y + 13 = 0$ ?
What is the distance of the point $(- 1, - 3)$ from the line $3 x + 4 y - 19 = 0$ ?
What is the distance of the point $(- 1, - 1)$ from the line $6 x + 8 y + 18 = 0$ ?
What is the distance of the point $(- 2, 4)$ from the line $8 x + 15 y - 2 = 0$ ?
Let $P (h, k)$ be a point with integer coordinates from which the two tangents to the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ are perpendicular to each other. How many such points $P$ are there?
A focal chord of the parabola $y^{2} = 16 x$ has length $25$ . What is the area of the triangle formed by this chord and the lines joining its end points to the vertex $O$ of the parabola?
A circle passes through the two foci of the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{9} = 1$ and through the end $(0, 3)$ of its minor axis. At what second point does the circle meet the $y$ -axis?
Through the point $(7, k)$ , three distinct real normals can be drawn to the parabola $y^{2} = 4 x$ . For how many integer values of $k$ is this possible?

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