Home
Class 12
MATHS
The tangent at any point to the circle x...

The tangent at any point to the circle `x^2+y^2=r^2` meets the coordinate axes at A and B.If the lines drawn parallel to axes through A and B meet at P then locus of P is

A

`((1)/(3),(1)/(sqrt(3)))`

B

`((1)/(4),(1)/(2))`

C

`((1)/(3),- (1)/(sqrt(3)))`

D

`((1)/(4), -(1)/(2))`

Text Solution

Verified by Experts


Let point P be `( cos theta , sin theta )`.
Tangent at P is `x cos theta + y sin theta =1`
`:. Q -= (1,(1cos theta )/(sin theta ))`
Normal at `P, y= tan theta x` (i)
Equation of QE` , y = (1-cos theta )/( sin theta )` (ii)
Point E is point of intersection of lines (i) and (ii) .
Eliminating `theta` from (i) and (ii), we get locus of point E.
From (i) , `tan theta = (y)/(x )`
From eq. (ii), we get
y=`(1-(x)/(sqrt(x^(2)+y^(2))))/((y)/(sqrt(x^(2)+y^(2))))=(sqrt(x^(2)+y^(2))-x)/(y)` ltbr. or `y^(2)+x= sqrt (x^(2)+y^(2))`
Clearly option (1) and (3) satisfy the above equation.
Promotional Banner

Similar Questions

Explore conceptually related problems

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

A tangent to the circle x^(2)+y^(2)=4 meets the coordinate axes at P and Q. The locus of midpoint of PQ is

The tangent at P, any point on the circle x^(2)+y^(2)=4, meets the coordinate axes in A and B, then (a) Length of AB is constant (b) P Aand PB are always equal (c) The locus of the midpoint of AB is x^(2)+y^(2)=x^(2)y^(2)(d) None of these

The tangent at P , any point on the circle x^2 +y^2 =4 , meets the coordinate axes in A and B , then (a) Length of AB is constant (b) PA and PB are always equal (c) The locus of the midpoint of AB is x^2 +y^2=x^2y^2 (d) None of these

If the tangent at any point of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) meets the coordinate axes in A and B, then show that the locus of mid-points of AB is a circle.

The tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve is