Home
Class 12
MATHS
A straight line is drawn through P(3,4) ...

A straight line is drawn through `P(3,4)` to meet the axis of `x` and `y` at `Aa n dB` , respectively. If the rectangle `O A C B` is completed, then find the locus of `Cdot`

Text Solution

Verified by Experts

The correct Answer is:
`(3)/(x)+(4)/(y)=1`
Let the point C be (h,k).
Then the coordinates of A and B are `(h,0) and 90,k)`, respectively, Since points A,P, and B are collinear, we have
`|{:(h,,0,,),(3,,4,,),(0,,k,,),(h,,0,,):}|=0`
or `4h+3k-hk=0`
or `4x+3y-xy=0`
Therefore, the required locus is `(3)/(x)+(4)/(y)=1`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Single)|59 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

A straight line is drawn through P(3,4) to meet the axis of x and y at A and B respectively.If the rectangle OACB is completed,then find the locus of C.

The variable line drawn through the point (1,3) meets the x -axis at A and y -axis at B .If the rectangle OAPB is completed.Where O isthe origin,then locus of ^(-)P' is

The variable line drawn through the point (1,3) meets the x-axis at A and y -axis at B .If the rectangle OAPB is completed.Where O is the origin,then locus of P is

A tangent is drawn to the parabola y^(2)=4ax at P such that it cuts the y-axis at Q. A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R. If the rectangle PQRS is completed, then find the locus of S.

The ends A and B of a straight line segment of constant length c slide upon the fixed rectangular axes OX and OY ,respectively.If the rectangle OAPB be completed,then the locus of the foot of the perpendicular drawn from P to AB is

Tongent and normal drawn to a parabola at A(at^(2),2at),t!=0 meet the x-axis at point BandD,respectively.If the rectangle ABCD is completed,then the locus of C is (a)y=2a (b) y+2a=c(c)x=2a (d) none of these

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q.If O is the origin and the rectangle OPRQ is completed then the locus of R is

A line passing through P(4,2) meet the X and Y -axes at A and B, respectively.If O is the origin,then locus of the centre of the circumference of triangle OAB is