Question

the number of lines drawn from the point (4,-5) so that it's distance from (-2,3) will be equal to 12 is​

Answer 1

Answer:

6x+8y=12

Step-by-step explanation:

(x2-x1)x-( y2- y1)y=12

-6x+8y=12

Answer 2

Answer:

No such line is possible that can be drawn from the point (4,-5).

Step-by-step explanation:

Equation of line through (4,-5) with slope of m is

= y + 5= m (x - 4)

= mx - y - 4m - 5 = 0

Then,

$\sf \bf \frac{ |m( - 2) - 3 - 4m - 5| }{ \sqrt{ {m}^{2} + 1} } = 12 \\ \\ : \implies \bf | - 6m - 8| = 12 \sqrt{( {m}^{2} + 1)}$

0n squaring both the side, we get :

(6m + 8)² = 144(m² + 1)

= 4(3m + 4)² = 144 (m² + 1)

= (3m + 4)² = 36 (m² + 1)

= 27m² - 24m + 20 = 0 .... (i)

Since, the discriminant of Equation (i) is (-24)² - 4.27.20 = -1584

Therefore, it's negative, there is no real value of m. Hence, no such line is possible.