Elliptical reflection

Geometry Level 4

If the equation of the curve obtained after reflection about the line x − y = 2 x-y= 2 of the ellipse ( x − 4 ) 2 16 + ( y − 3 ) 2 9 = 1 \dfrac{(x-4)^2}{16} + \dfrac{(y-3)^2}9 = 1 is 16 x 2 + 9 y 2 + k 1 x − 36 y + k 2 = 0 16x^2 + 9y^2 + k_1 x - 36y + k_2 = 0 , where k 1 k_1 and k 2 k_2 are constants.

Evaluate k 1 + k 2 k_1 + k_2 .


The answer is 132.

Avi Solanki by avi solanki , 23, India

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2 solutions

Archit Agrawal
Jan 21, 2017

As line is at 45°, so replace x and y and shift centre by taking its image about this line you will get the locus as 16(x-5)^2+9(y-2)^2=144.

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yes @Archit Agrawal .great solution

avi solanki - 4 years, 4 months ago
Avi Solanki
Jan 20, 2017

Any point on the curve is 4(1+cosx) ,3(1+sinx) .find the reflection of this point about the line and then find locus of that point .

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