Conic Sections Question 413
Question: The locus of the point of intersection of the lines $ bxt-ayt=ab $ and $ bx+ay=abt $ is
Options:
A) A parabola is a U-shaped curve where any point is at an equal distance from the focus and directrix. It is defined as the set of all points equidistant from a fixed point (focus) and a fixed line (directrix). The standard form of a parabola that opens upward is y = ax² + bx + c, where a ≠ 0.
B) An ellipse is a closed curve traced by a point moving in a plane such that the sum of the distances from two fixed points (foci) is constant.
C) A hyperbola is a conic section formed by the intersection of a plane with a double-napped cone, where the plane intersects both nappes. It consists of two separate branches and has two asymptotes.
D) None of these
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Answer:
Correct Answer: C
Solution:
Multiplying both, we get $ {{(bx)}^{2}}-{{(ay)}^{2}}={{(b^{2}x^{2})}-{{(a^{2}y^{2})}} $
therefore $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ which is the standard equation of hyperbola.
BETA
