30 Questions
What is the coordinate of the point P on the ellipse?
(0, 4)
What is the value of e in the given ellipse?
3/5
What is the equation of the reflected ray after first reflection?
4x + 3y = 12
What is the coordinate of the focus S?
(3, 0)
What is the shape of the mirror that reflects the light ray towards the other focus?
Elliptical
What is the slope of the normal at the point P?
3/4
What is the property of the ellipse that is used to find the reflected ray?
The sum of the distances from the two foci is constant.
What is the equation of the ellipse?
16x^2 + 25y^2 = 400
What is the point of incidence of the light ray?
(0, 4)
What is the direction of the reflected ray?
Towards the focus S
What is the equation of the diameter bisecting the chords of slope m of the ellipse?
y = mx + c
What is the angle between the conjugate diameters of an ellipse?
greater than 90°
What is the condition for two diameters of an ellipse to be conjugate?
each bisects all chords parallel to the other
What is the relationship between the slopes of two conjugate diameters of an ellipse?
m1m2 = 1
What is the property of the tangent at the extremity of any diameter of an ellipse?
it is parallel to the chords it bisects
What is the sum of the squares of any two conjugate semi-diameters of an ellipse?
constant and equal to the sum of the squares of the semi-axes of the ellipse
What is the relationship between the eccentric angles of the ends of a pair of conjugate diameters of an ellipse?
they differ by a right angle
What is the condition for two diameters of a circle to be conjugate?
each is perpendicular to the other
What is the equation of the diameter passing through the origin of the ellipse?
y = -x
What is the property of the tangent at the ends of any chord of an ellipse?
it meets on the diameter which bisects the chord
What is the equation of the ellipse in the standard form?
x2/a2 + y2/b2 = 1
What is the value of cos(θ - φ) in the parametric equation of the ellipse?
0
What is the length of the subnormal at the point P(x1, y1) to the ellipse?
x1/a
What is the relationship between the eccentric angle θ and the focal distance of the ellipse?
θ = tan^-1(y1/x1)
What is the special form of the ellipse when a = b?
Circle
What is the equation of the tangent at the point P(x1, y1) to the ellipse?
y1/x1 = -x/y
What is the relationship between the slopes of the tangent and normal at the point P(x1, y1) to the ellipse?
m1 = -1/m2
What is the value of x1 in the parametric equation of the ellipse?
a cos θ
What is the length of the subtangent at the point P(x1, y1) to the ellipse?
sqrt(x1^2/a2 - y1^2/b2)
What is the equation of the normal at the point P(x1, y1) to the ellipse?
y1/x1 = -y/x
Test your understanding of conic sections, specifically ellipses, with this quiz. Questions cover equations, tangents, and more.
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