Math, asked by rishita4757, 2 months ago

the length of the chord formed by x^2+y^2=a^2 on the line x cos alpha + y sin alpha = p is​

Answers

Answered by gautrisharma6
1

Answer:

I can't solve_______________

Answered by amitnrw
1

Given : chord formed by x^2+y^2=a^2 on the line x cos alpha + y sin alpha = p

To Find : Length of chord

Solution:

circle x² + y² = a²

center O = ( 0 , 0)

Radius = a

A and B are the end points of chord

Then M is the mid point of chord

AM = BM = AB/2

AM² + OM²  = OA²   or BM² + OM²  = OB²

OA = OB = Radius = a

OM ⊥  AB

Hence perpendicular distance of O(0,0) from   x cosα + y sinα = p

 x cosα + y sinα -  p  = 0     point (0, 0)

=  |   (0 * cosα + 0 *  sinα   - p )  / (cos²α +  sin²α) |

cos²α +  sin²α = 1

= | - p / 1|

= | - p|

OM =  | - p|

OM² = p²

AM² + p²  = a²

=> AM² = a²  -  p²

=> AM = √a²  -  p²

2AM = 2√a²  -  p²

=> AB = 2√a²  -  p²

Hence length of the chord formed = 2√a²  -  p²

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