Class 11th Mathematics Unit Test: Straight Lines, Circle, Conic Section, Set and Relation

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Which conic section is represented by the equation $3x^2 + 4y^2 - 12x + 16y - 20 = 0$?

Ellipse (correct)

Hyperbola

Circle

Parabola

Which of the following represents the equation of a straight line passing through the point (3, 4) and perpendicular to the line $2x - 3y + 5 = 0$?

$2x + 3y - 1 = 0$

$2x - 3y - 11 = 0

$3x + 2y - 5 = 0$

$3x - 2y - 5 = 0$ (correct)

For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the circle?

$(x - 2)^2 + (y + 3)^2 = 20$

$(x - 4)^2 + (y - 1)^2 = 20$

$(x - 2)^2 + (y + 3)^2 = 16$ (correct)

$(x - 4)^2 + (y - 1)^2 = 16$

What is the equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1)?

$x + y - 3 = 0$ Signup and view all the answers

Find the equation of the ellipse with foci at (1, 2) and (-1, 2) passing through the point (3, 2).

$rac{x^2}{4} + rac{(y-2)^2}{3} = 1$ Signup and view all the answers

Determine the equation of the parabola with focus at (3, 4) and directrix $y = -2$.

$(x-3)^2 = 8(y+2)$ Signup and view all the answers

Given the equation of the hyperbola $9x^2 - 16y^2 - 36x + 64y - 71 = 0$, find the coordinates of the center and vertices.

Center: (2, -2), Vertices: (5, -2) and (-1, -2) Signup and view all the answers

The equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1) is a ______ line

straight Signup and view all the answers

Find the equation of the ______ with foci at (1, 2) and (-1, 2) passing through the point (3, 2)

ellipse Signup and view all the answers

Determine the equation of the ______ with focus at (3, 4) and directrix $y = -2$

parabola Signup and view all the answers

For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the ______?

circle Signup and view all the answers

Class 11th Mathematics Unit Test: Straight Lines, Circle, Conic Section, Set and Relation

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Questions and Answers

Which conic section is represented by the equation $3x^2 + 4y^2 - 12x + 16y - 20 = 0$?

Which of the following represents the equation of a straight line passing through the point (3, 4) and perpendicular to the line $2x - 3y + 5 = 0$?

For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the circle?

What is the equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1)?

Find the equation of the ellipse with foci at (1, 2) and (-1, 2) passing through the point (3, 2).

Determine the equation of the parabola with focus at (3, 4) and directrix $y = -2$.

Given the equation of the hyperbola $9x^2 - 16y^2 - 36x + 64y - 71 = 0$, find the coordinates of the center and vertices.

The equation of the tangent to the circle $x^2 + y^2 - 6x + 8y - 5 = 0$ at the point (1, -1) is a ______ line

Find the equation of the ______ with foci at (1, 2) and (-1, 2) passing through the point (3, 2)

Determine the equation of the ______ with focus at (3, 4) and directrix $y = -2$

For the circle with center (2, -3) and passing through the point (4, 1), what is the equation of the ______?

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