Question

Find the distance between P(x, y) and Q (x, y,) when : (i) PQ is parallel to the -axis, (ii) PQ is parallel to the x-axis.​

Answer 1

Answer:

Equation of line with slope m passing through point (4,−5) is given by,

y+5=m(x−4)⇒mx−y−4m−5=0

Given distance of above line from the point (−2,3) is 12

⇒

∣

∣

∣

∣

∣

m

2

+1

m(−2)−3−4m−5

∣

∣

∣

∣

∣

=12

⇒

∣

∣

∣

∣

∣

m

2

+1

3m+4

∣

∣

∣

∣

∣

=6

⇒(3m+4)

2

=36(m

2

+1), square both sides

⇒27m

2

−24m+20=0

Discriminant of of above quadratic is, (−24)

2

−4⋅27⋅20=−1584<0

Hence, there no real root of above quadratic.

i.e. there does not exist any line at a distance 12 from the point (−2,3)

and passing through the point (4,−5)