For the curve x 2 + y 2 − 4 x − 4 y − 1 = 0 at the point P whose ordinate is 5, match the following. (a) y-intercept of the tangent at P (p) 2 (b) x-intercept of the normal at P (q) 10 (c) Area of the

Question

For the curve x 2 + y 2 − 4 x − 4 y − 1 = 0 at the point P whose ordinate is 5, match the following. (a) y-intercept of the tangent at P (p) 2 (b) x-intercept of the normal at P (q) 10 (c) Area of the quadrilateral formed by the tangent and normal at P and the co-ordinate axes (r) 1 (d) A tangent to the curve is drawn parallel to the tangent at P. Its distance from the origin is (s) 5

TestHub · Accepted Answer

Put y = 5 : x 2 − 4 x + 4 = 0 , so P = ( 2 , 5 ) ; centre ( 2 , 2 ) , radius 3. The tangent at P is y = 5 and the normal is x = 2 . (a) y-intercept of tangent = 5 (s). (b) x-intercept of normal = 2 (p). (c) The quadrilateral is a rectangle with sides 2 and 5, area 10 (q). (d) The other parallel tangent is y = − 1 , at distance 1 from the origin (r).

Mathematics - Application of Derivative Question with Solution | TestHub

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Doubts & Discussion

(a) y-intercept of the tangent at P	(p) 2
(b) x-intercept of the normal at P	(q) 10
(c) Area of the quadrilateral formed by the tangent and normal at P and the co-ordinate axes	(r) 1
(d) A tangent to the curve is drawn parallel to the tangent at P. Its distance from the origin is	(s) 5