Question 14 (OR 1st Question) If tangent to the curve y2 + 3x β 7 = 0 at the point (β, k) is parallel to line x β y = 4, then value of k is ______?
We know that
Slope of tangent is ππ¦/ππ₯
Now,
y2 + 3x β 7 = 0
Differentiating w.r.t.π₯
2yππ¦/ππ₯ + 3 β 0 = 0
2yππ¦/ππ₯ + 3 = 0
2yππ¦/ππ₯ = β3
ππ¦/ππ₯ = (β3)/2π¦
At point (h, k)
Slope is
ππ¦/ππ₯ = (β3)/2π
Now, finding slope of line x β y = 4
x β y = 4
x β 4 = y
y = x β 4
Comparing with y = mx + c
So, slope of line is 1
Since tangent and line are parallel
Slope of tangent = 1
ππ¦/ππ₯ = 1
(β3)/2π = 1
β3 = 2k
(β3)/2 = k
k = (βπ)/π

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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