IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

deep01

A point P(

3,1) moves on a circle x²+y²=4 and after covering a quarter of the circle leaves it tangentially.The equation of a line along which the point moves after leaving the circle is:

(A)y=

3x+4 (B)

3y=x+4

(C)

3y=x-4 (D)y=

3x-4

rajat

it is B , C

actually i am getting

^{[2 ]}

3y = -x +- 4

in stead of sqroot(3)y = x +-4

rinkupark

it is (a)

siddharthsaxena

it is b,c for sure.

siddharthsaxena

it is b,c for sure.

amar.gupta

Let the center of the circle be O i.e. (0,0) and P moves quarter of the circle i.e. 90 degree to reach at point Q. Then OP and OQ will be perpendicular to each other.

Let Q (h,k)

then slope of OP = 1/

3

and slope of OQ =k/h

so (1/

3) (k/h) =-1

or k= -

3h.......[1]

since Q will be on the circle. so h^2+k^2 =4..........[2]

from [1] and [2] : h=1 and k= -

3 or h= -1 and k=

3

so Q : (1,-

3) or (-1,

3)

now eq. of tangent at Q :

x-

3y=4 and -x+

3y=4

amar.gupta

rajat

sooorrry it is A,D 100 % sure

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