30 Questions
What is the pole of the line 2x = y with respect to the parabola y² = 2x?
(0, 2)
What is the equation of the polar of a point (x₁, y₁) with respect to the circle x² + y² = 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
What is the equation of the tangent to the parabola y² = 4ax at the point (x₁, y₁)?
yy₁ = x + x₁
What is the equation of the polar of a point (x, y) with respect to the parabola y² = 4ax?
lx + my + n = 0
What is the pole of the line lx + my + n = 0 with respect to the parabola y² = 4ax?
(am, n/l)
What is the equation of the polar of the point (x1, y1) with respect to the parabola y² = 4ax?
yy1 = 2a(x + x1)
What is the equation of the polar of the focus of the parabola y² = 4ax?
x + a = 0
What is the chord that passes through the focus and is perpendicular to the axis?
Latus-rectum
What is the point that bisects every chord of the conic passing through it?
Centre
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
What is the focus of the parabola y^2 = 4ax?
(a, 0)
What is the axis of the parabola y^2 = 4ax?
x-axis
What is the focal distance of the parabola y^2 = 4ax?
a
What is the vertex of the parabola y^2 = 4ax?
(0, 0)
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)
What is the focal distance of a parabola with the equation y^2 = 4ax?
2a
What is the vertex of a parabola in standard form y² = 4ax?
(a, 0)
What is the axis of a parabola in standard form y² = 4ax?
x-axis
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
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)
What is the focal distance of a parabola with the equation y² = 4ax?
a
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)
What is the vertex of a parabola with the equation (x - h)² = 4a(y - k)?
(h, k)
What is the equation of a parabola with its axis parallel to the x-axis and focus at the origin?
y² = 4ax
What is the focal distance of the parabola y² = 4ax?
a
What is the equation of the directrix of the parabola y² = 4ax?
x + a = 0
What is the vertex of the parabola y² = 4ax?
(0, 0)
What is the axis of the parabola y² = 4ax?
x-axis
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)
Test your understanding of conic sections with this quiz on pole and polar coordinates. Learn about the relationship between tangents, poles, and chords in parabolas.
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