Home
Class 12
MATHS
Let P be a point on the circle x^(2) + ...

Let P be a point on the circle `x^(2) + y^(2) = a^(2)` whose ordinate is PN and Q is a point on PN such that PN : QN = 2 : 1 . Find the locus of Q and identify it

Text Solution

Verified by Experts

The correct Answer is:
Therefore, required equation to the locus of P is `x^(2) + 4y^(2) = a^(2) ` , which represents an ellipse .
Promotional Banner

Topper's Solved these Questions

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBHS Archive (2013)|15 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise WBHS Archive (2014)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion - Reason Type)|2 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION ( ASSERTION-REASON TYPE )|2 Videos

Similar Questions

Explore conceptually related problems

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot

Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter, such that P is nearest to the line y=2xdot Find the locus of Pdot

Let P be a point on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and the line through P parallel to the y-axis meets the circle x^(2)+y^(2)=9 at Q, where P,Q are on the same side of the x-axis. If R is a point on PQ such that (PR)/(RQ)=(1)/(2) , then the locus of R is

Let P b any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 whose ordinate is PN. AA′ is its transverse axis. If the point Q divides AP in the ratio a^(2):b^(2) , then NQ is?

Let , RS be the diameter of the circle x^(2) + y^(2) = 1 , where S is the point ( 1,0) . Let P be a variable point (other then R and S ) on the circle and tangents to the circle at s and P meet at the point Q . The normal to the circle at P intersects a line drawn through Q parallel to RS at point E . The locus of E passes through the point (s)

If P be any point on the plane lx+my+nz=p and Q be a point on the line OP such that OP.OQ=p^(2) , then find the locus of the point Q.

Let O be the vertex and Q be any point on the parabola x^(2) = 8 y . If the point P divides the line segments OQ internally in the ratio 1 : 3 , then the locus of P is _

PN is any ordinate of the parabola y^(2) = 4ax , the point M divides PN in the ratio m: n . Find the locus of M .

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is