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let P(x,y) be a point and let me a line if l(h,k) is the foot of perpendicular drawn from be on this line and q(Alpha, beta) is image of P in the given line then prove that (h-x)/a=(k-y)/b=-(ax+by+c)/(a^2+b^2)

let P(x,y) be a point and let me a line if l(h,k) is the foot of perpendicular drawn from be on this line and q(Alpha, beta) is image of P in the given line then prove that (h-x)/a=(k-y)/b=-(ax+by+c)/(a^2+b^2)

Grade:11

3 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Dear student

Please write the Question in a standard form or attach an image of the question

Regards
Vikas TU
14149 Points
one year ago
Dear student 
Question is not clear 
Please attach an image, 
We will happy to  help you 
Good Luck
Cheers
Arun
25763 Points
one year ago
Let P(h, k) be the given point, let Q(x, y) be the foot of the perpendicular, and let O be the origin. The line can have any direction.  
∠PQO = 90°  
Point Q lies on the circle having diameter OP.  
The locus of point Q:  
(x - 0)(x - h) + (y - 0)(y - k) = 0  
x² + y² - hx - ky = 0
 
 

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