NCERT Class 11-Math's: Exemplar Chapter –11 Conic Sections Part 5
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Question 13:
The area of the triangle formed by the lines joining the vertex of the parabola to the ends of its latus rectum is
Vertex of the Parabola
(A) . units
(B) . units
(C) . units
(D) . units
Answer:
The correct option is (C).
From the figure, OPQ represent the triangle whose area is to be determined. The area of the triangle
Question 14:
The equations of the lines joining the vertex of the parabola to the points on it which have abscissa are
(A)
(B)
(C)
(D)
Answer:
(B) is the correct choice.
Let P and Q be points on the parabola and OP, OQ be the lines joining the vertex O to the points P and Q whose abscissa are 24.
Points on the Parabola
Thus
or .
Therefore the coordinates of the points P and Q are and respectively. Hence the lines are
Question 15:
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points and is
(A)
(B)
(C)
(D)
Answer:
(B) is the correct choice.
Let be the equation of the ellipse. Then according to the given conditions, we have
Which gives
Hence, required equation of ellipse is .
Question 16:
The length of the transverse axis along x-axis with centre at origin of a hyperbola is and it passes through the point . The equation of the hyperbola is
(A)
(B)
(C)
(D) None of these
Answer:
(C) Is the correct choice.
Let represent the hyperbola. Then according to the given condition, the length of transverse axis, i.e., .
Also, the point lies on the hyperbola, so, we have
which gives
Hence, the equation of the hyperbola is