Question

The point on the line 4x - y - 2 = 0 is (a, b) which is equidistant from (-5, 6) and (3, 2) then
a^2 + B^2=
​

Answer 1

Answer:

200

Step-by-step explanation:

As ( a, b ) lies on 4x - y - 2 = 0,

= > 4(a) - (b) - 2 = 0

= > 4a - b - 2 = 0

= > 4a - 2 = b ... (1)

As it is equidistant from the given points.

= > distance b/w ( - 5, 6 ) and ( a, b ) = distance b/w ( 3, 2 ) and ( a, b )

Using distance formula,

= > √{ ( - 5 - a )² + ( 6 - b )² } = √{ ( 3 - a )² + ( 2 - b )² }

= > ( - 5 - a )² + ( 6 - b )² = ( 3 - a )² + ( 2 - b )^2

= > 25 + a² + 10a + 36 + b² - 12b = 9 + a² - 6a + 4 + b² - 4b

= > 16a - 8b = - 48

= > 2a - b = - 6

= > 2a - 4a + 2 = - 6 { b = 4a - 2 }

= > a = 4

Hence, b = 4(4) - 2 = 14

Therefore,

a² + b² = (4)² + (14)² = 16 + 196 = 200