Maths-
General
Easy
Question
Statement- (1) : PQ is a focal chord of a parabola. Then the tangent at P to the parabola is parallel to the normal at Q.
Statement- (2) : If P(t1) and Q(t2) are the ends of a focal chord of the parabola y2 = 4ax, then t1t2 = –1.
- Both S1 & S2 are correct & S2 is correct explanation of S1
- Both S1 & S2 are correct but S2 is not correct explanation of S1
- S1 is correct S2 is wrong
- S1 is wrong S2 is correct
Hint:
properties of tangent and normal of a parabola.
The correct answer is: Both S1 & S2 are correct & S2 is correct explanation of S1
Both S1 & S2 are correct & S2 is correct explanation of S1
equation of tangent at P : t1y = x+at2
equation of normal at Q : y+ xt2 = 2at2 + at23
the slopes at P and Q are 1/t1 and -t2 respectively
slopes at the two extremeties of a focal chord are : (t,-1/t)
this property is used to explain the behaviour of tangents and normals at the respective points.
Related Questions to study
maths-
Statement- (1) : Let (
) and (
) are the ends of a focal chord of 
= 4x then 
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then SP + SQ = 2
.
Statement- (1) : Let () and () are the ends of a focal chord of = 4x then
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.
Statement- (1) : If 4 & 3 are length of two focal segments of focal chord of parabola y2 = 4ax than latus rectum of parabola will be 48/7 units
Statement- (2) : If 1 & 2 are length of focal segments of focal chord than its latus rectum is .
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An alternating current of frequency 200 rad/sec and peak value 1A as shown in the figure, is applied to the primary of a transformer. If the coefficient of mutual induction between the primary and the secondary is 1.5 H, the voltage induced in the secondary will be
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