The slope of tangent m=tan45∘=1 Now, 5x2−9y2−20x−18y−34=10 ⇒5(x2−4x)−9(y2+2y)=34 ⇒5(x2−4x+4)−9(y2+2y+1)=34+20−9 ⇒5(x−2)2−9(y+1)2=45 ⇒
(x−2)2
9
−
(y+1)2
5
=1 The equation of the tangent with slope m is y+1=m(x−2)±√9m2−5 Since, m=1 ⇒y+1=(x−2)±√9−5 ⇒y=x−1 or y=x−5 ⇒ The equation x−y−1=0 or x−y−5=0 Comparing with x+by+c=0 ⇒b=−1 and c=−1,−5 ⇒b2+c2=(−1)2+(−1)2=1+1=2 and b2+c2=(−1)2+(−5)2=1+25=26 ⇒b2+c2=2 or 26
