X
P and Q are two variable points on the axes of
and y respectively such that
OP + |OQ=a, then the locus of foot of
perpendicular from origin on PQ is
1) (x - y) (x2 + y2) = axy
2) (x + y) (x2 + y²) = axy
3) (x + y) (x2 + y²) = a (x - y)
4) (x + y) (x2 - y²) = axy
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Asked on December 26, 2019 by
Sarif Sachdeva
The locus of the foot of the perpendiculars drawn from the vertex on variable tangent to the parabola y
2
=4ax is:
A
x(x
2
+y
2
)+ay
2
=0
B
y(x
2
+y
2
)+ax
2
=0
C
x(x
2
−y
2
)+ay
2
=0
D
none of these
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ANSWER
Tangent at (at
2
,2at) is given by ty=x+at
2
Slope of OP× Slope of tangent=−1
h
b
×
t
1
=−1
k=−ht
⇒t=
h
−k
(h,k) is a tangent,
⇒kt=h+at
2
⇒k(−
h
k
)=h+a(
h
2
k
2
)
⇒−k
2
h=h
3
+ab
2
⇒x
3
+ay
2
+xy
2
=0
⇒x(x
2
+y
2
)+ay
2
=0
⇒(A).
solution
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