Question 14 (OR 1st Question) If tangent to the curve y2 + 3x โ 7 = 0 at the point (โ, k) is parallel to line x โ y = 4, then value of k is ______?
We know that
Slope of tangent is ๐๐ฆ/๐๐ฅ
Now,
y2 + 3x โ 7 = 0
Differentiating w.r.t.๐ฅ
2y๐๐ฆ/๐๐ฅ + 3 โ 0 = 0
2y๐๐ฆ/๐๐ฅ + 3 = 0
2y๐๐ฆ/๐๐ฅ = โ3
๐๐ฆ/๐๐ฅ = (โ3)/2๐ฆ
At point (h, k)
Slope is
๐๐ฆ/๐๐ฅ = (โ3)/2๐
Now, finding slope of line x โ y = 4
x โ y = 4
x โ 4 = y
y = x โ 4
Comparing with y = mx + c
So, slope of line is 1
Since tangent and line are parallel
Slope of tangent = 1
๐๐ฆ/๐๐ฅ = 1
(โ3)/2๐ = 1
โ3 = 2k
(โ3)/2 = k
k = (โ๐)/๐

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.