Parabola

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What is the pole of the line 2x = y with respect to the parabola y² = 2x?

(0, 2) (correct)

(0, 1/2)

(1, 0)

(-1, 0)

What is the equation of the polar of a point (x₁, y₁) with respect to the circle x² + y² = r²?

xx₁ - yy₁ = r²

xx₁ + yy₁ = r² (correct)

yy₁ - xx₁ = r²

xx₁ + yy₁ = -r²

If the polar of a point with respect to the circle x² + y² = r² touches the parabola y² = 4ax, what is the locus of the pole?

x² = -ry/a

y² = rx/a

y² = 2rx/a

x² = ry/a (correct)

What is the equation of the tangent to the parabola y² = 4ax at the point (x₁, y₁)?

yy₁ = x + x₁ Signup and view all the answers

What is the equation of the polar of a point (x, y) with respect to the parabola y² = 4ax?

lx + my + n = 0 Signup and view all the answers

What is the pole of the line lx + my + n = 0 with respect to the parabola y² = 4ax?

(am, n/l) Signup and view all the answers

What is the equation of the polar of the point (x1, y1) with respect to the parabola y² = 4ax?

yy1 = 2a(x + x1) Signup and view all the answers

What is the equation of the polar of the focus of the parabola y² = 4ax?

x + a = 0 Signup and view all the answers

What is the chord that passes through the focus and is perpendicular to the axis?

Latus-rectum Signup and view all the answers

What is the point that bisects every chord of the conic passing through it?

Centre Signup and view all the answers

What is the equation of the parabola in standard form when AS = AK = a(> 0) and the coordinate of S is (a, 0)?

y^2 = 4ax Signup and view all the answers

What is the focus of the parabola y^2 = 4ax?

(a, 0) Signup and view all the answers

What is the axis of the parabola y^2 = 4ax?

x-axis Signup and view all the answers

What is the focal distance of the parabola y^2 = 4ax?

a Signup and view all the answers

What is the vertex of the parabola y^2 = 4ax?

(0, 0) Signup and view all the answers

What is the equation of a parabola with its vertex at (h, k) and axis parallel to the x-axis?

(y - k)^2 = 4a(x - h) Signup and view all the answers

What is the focal distance of a parabola with the equation y^2 = 4ax?

2a Signup and view all the answers

What is the vertex of a parabola in standard form y² = 4ax?

(a, 0) Signup and view all the answers

What is the axis of a parabola in standard form y² = 4ax?

x-axis Signup and view all the answers

What is the general equation of a parabola in standard form when AS = AK = a (> 0) and the coordinate of S is (a, 0)?

y² = 4ax Signup and view all the answers

What is the equation of a parabola with its vertex at (h, k) and axis parallel to the y-axis?

(x - h)² = 4b(y - k) Signup and view all the answers

What is the focal distance of a parabola with the equation y² = 4ax?

a Signup and view all the answers

What is the equation of a parabola in standard form when its vertex and focus are on the x-axis at a distance a and a' respectively from the origin?

y² = 4(a' - a)(x - a) Signup and view all the answers

What is the vertex of a parabola with the equation (x - h)² = 4a(y - k)?

(h, k) Signup and view all the answers

What is the equation of a parabola with its axis parallel to the x-axis and focus at the origin?

y² = 4ax Signup and view all the answers

What is the focal distance of the parabola y² = 4ax?

a Signup and view all the answers

What is the equation of the directrix of the parabola y² = 4ax?

x + a = 0 Signup and view all the answers

What is the vertex of the parabola y² = 4ax?

(0, 0) Signup and view all the answers

What is the axis of the parabola y² = 4ax?

x-axis Signup and view all the answers

In the parabola y² = 4ax, what is the standard form of the equation when AS = AK = a (> 0) and the coordinate of S is (a, 0)?

(x - a)² = 4a(y - 0) Signup and view all the answers

Parabola

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Questions and Answers

What is the pole of the line 2x = y with respect to the parabola y² = 2x?

What is the equation of the polar of a point (x₁, y₁) with respect to the circle x² + y² = r²?

If the polar of a point with respect to the circle x² + y² = r² touches the parabola y² = 4ax, what is the locus of the pole?

What is the equation of the tangent to the parabola y² = 4ax at the point (x₁, y₁)?

What is the equation of the polar of a point (x, y) with respect to the parabola y² = 4ax?

What is the pole of the line lx + my + n = 0 with respect to the parabola y² = 4ax?

What is the equation of the polar of the point (x1, y1) with respect to the parabola y² = 4ax?

What is the equation of the polar of the focus of the parabola y² = 4ax?

What is the chord that passes through the focus and is perpendicular to the axis?

What is the point that bisects every chord of the conic passing through it?

What is the equation of the parabola in standard form when AS = AK = a(> 0) and the coordinate of S is (a, 0)?

What is the focus of the parabola y^2 = 4ax?

What is the axis of the parabola y^2 = 4ax?

What is the focal distance of the parabola y^2 = 4ax?

What is the vertex of the parabola y^2 = 4ax?

What is the equation of a parabola with its vertex at (h, k) and axis parallel to the x-axis?

What is the focal distance of a parabola with the equation y^2 = 4ax?

What is the vertex of a parabola in standard form y² = 4ax?

What is the axis of a parabola in standard form y² = 4ax?

What is the general equation of a parabola in standard form when AS = AK = a (> 0) and the coordinate of S is (a, 0)?

What is the equation of a parabola with its vertex at (h, k) and axis parallel to the y-axis?

What is the focal distance of a parabola with the equation y² = 4ax?

What is the equation of a parabola in standard form when its vertex and focus are on the x-axis at a distance a and a' respectively from the origin?

What is the vertex of a parabola with the equation (x - h)² = 4a(y - k)?

What is the equation of a parabola with its axis parallel to the x-axis and focus at the origin?

What is the focal distance of the parabola y² = 4ax?

What is the equation of the directrix of the parabola y² = 4ax?

What is the vertex of the parabola y² = 4ax?

What is the axis of the parabola y² = 4ax?

In the parabola y² = 4ax, what is the standard form of the equation when AS = AK = a (> 0) and the coordinate of S is (a, 0)?

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