Grade 12Trigonometry

The locus of centre of circle which cuts a chord of length 2a from the positive x axis and passes through a point on positive y axis distance b from the origin is?
Ans is x^2+2by=a^2-b^2 but how?

sanvy

8 Years agoGrade 12

3 Answers

Prajwal

8 Years ago

We know length of intercept made by circle on X axis is √(G ²-C )= 2A

AND. Length of intercept made by circle on y axis is √(F ² --c)=b

Just do the squaring and add them you will get the same equation

Prajwal

Approved Tutor Answer8 Years ago

Correction the legenth of intercept are 2√g^2-c

And 2√f^2-c it is not same as given above so you will get g^2-c=a^2 and f^2-c=b^2/2

SURYANSH SINGH RAWAT

8 Years ago

=>2✓g²-c = 2a => g²-c = a².........(1)Now let the equation of circle be x²+y²+2gx+2fy+c=0 It passes through (0,b) so,=> b²+2fb+c=0 .......(2)Here (-g,-f) is (h,k) By solving (1) & (2) by eliminating `c` we get the required equation of the ellipse i.e [x²-2yb+b²=a²]