Question

ABC is right angled at C. if P is the length of the perpendicular form C to AB sides opposite angel A, angle B, angle C respectively then prove that ¹/p²=1/a²+1/b²​

Answer 1

Answer:

Slope of the line is 2 and passes through A(1, 3)

x−1

y−3

=2

y−3=2x−2

y=2x+1

(a) For point B(3, 7)

2(3) + 1 = 7

Hence the point B(3, 7)lies on the line y = 2x + 1

(b) Equation of the line is y = 2x+1.

(c) Let (x

1

,y

1

) be the coordinates of point C on line.

Therefore it satisfies the equation of line a y=2x+1

∴y

1

=2x

1

+1

BC=2AB

⇒

(x

1

−3)

2

+(y

1

−7)

2

=2

(3−1)

2

+(7−3)

2

Squaring both sides, we get

⇒(x

1

−3)

2

+(y

1

−7)

2

=4[(3−1)

2

+(7−3)

2

]

(x

1

−3)

2

+(2x

1

+1−7)

2

=4[(2)

2

+(4)

2

] [∴y

1

=2x

1

+1]

5(x

1

−3)

2

=80

(x

1

−3)

2

=16

x

1

−3=±4

x

1

=7 or −1

y

1

=2x

1

+1=2(7)+1=15

y

1

=2x

1

+1=2(−1)+1=−1

The coordinates of point C are (7,15) or (−1,−1),,