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Identities Used :-
Let assume that line y = mx + 1 toches the curve y² = 4x at point P (x, y).
Now
Given that,
On differentiating both sides w. r. t. x, we get
Therefore, slope of tangent at point P(x, y) is
Also,
- Its given that y = mx + 1 is a tangent to the curve (1),
- Slope of line, y = mx + 1 is 'm' ----(3)
So,
From equation (2) and equation (3), we concluded that
Now, Substitute the value of y in y = mx + c, we get
Therefore, point of contact of tangent with the given curve (1) is
Now,
As P lies on the curve (1), we get
Additional Information :-
- 1. Two lines having slope m and M respectively are parallel iff m = M.
- 2. Two lines having slope m and M respectively are perpendicular to each other iff Mm = - 1.
- 3. If line is parallel to x axis, then slope is 0.
- 4. If line is parallel to y axis, then slope is not defined.
- 5. If tangent make equal intercept on the axes, then slope is 1 or - 1.
- 6. If line bisects the quarants, then slope is 1 or - 1.
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