y 2 = 4ax ⇒ =

y = ⇒ =

= y

Product of slopes = = – 1 = = – 1

1 ≤ | sin x | + | cos x | ≤

y = [| sin x | + | cos x|]

⇒ y = 1

P(2, 1)

x 2 + y 2 = 5

=

tan θ =

cosec 2 θ =

Let y 2 = 4a (x + a) ........(1)

and y 2 = 4b (x + b) .........(2)

intersect each other at (h, k) then h = – (b + a)

Now for curve (1) is and for curve (2) is

⇒ × = –1 ⇒ = –1

⇒ = –1 ⇒ = –1 ⇒ = –1

Which is always true

⇒ can take any value from interval

Inverse curves touches each other at line y = x

⇒ y = x is tangent to both curves ⇒ equation x = x 2 + 3x + c has both equal roots

⇒ c = 1 and x = –1 = h and y = –1 = k ⇒ |h + k + c| = 1