Question

if the foot of the perpendicular from (-4, 5) to the straight line 3x-4y-18=0 is ( alfa, beta) then the value of alfa+ beta is​

Answer 1

Step-by-step explanation:

Slope of the line joining two points (−4,5)(−4,5) and (α,β)(α,β) must be equal to −43−43. 

⇒β−5α+4=−43⇒β−5α+4=−43

4α+3β=−1……(1)4α+3β=−1……(1)

And (α,β)(α,β) also satisfy the give equation of line.

⇒3α−4β=18……(2)⇒3α−4β=18……(2)

From 11 and 22

28(α+β)−7β=−728(α+β)−7β=−7

3(α+β)−7β=183(α+β)−7β=18

alpha+beta= -1

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