Question

please answer this question of circles chapter, class 11
the answer should be with detailed explanation

best answer will surely be marked as brainliest ​

Answer 1

Answer:

3

Step-by-step explanation:

Let the center C (h , k )

Rods are sliding on axis , let rods are AB and PQ .

Now perpendicular to chord from centre bisects it so lengths PM and AN will be b/2 and p/q . respectively .

CP and CN are radius of circle .

Let CP = CN = r

Since coordinates of centre are ( h , k ) , which is nothing but distance from coordinate axes .

So , CN = h and CM = k

Now use Pythagoras in two Right angle triangles , ∆CAN and ∆CMP

${r}^{2} = {h}^{2} + {( \frac{a}{2} )}^{2} \\ \\ {r}^{2} = {k}^{2} + { (\frac{b}{2} )}^{2}$

Subtract both equations and eliminate r .

${h}^{2} - {k}^{2} + \frac{ {a}^{2} }{4} - \frac{ {b}^{2} }{4} = 0 \\ \\ 4( {x}^{2} - {y}^{2} ) = {b}^{2} - {a}^{2}$

** If you take x - axis rode as a , you will get a^2 - b^2 , but both answers are correct since it is not mention which rod is on which axis.