{\f}( {\x}) is a continuous function on \mathbb{R} and {\y}= {\f}( {\x}) is a curve. If (\alpha, \beta) is a point such that \beta= {\f}(\alpha) and p \alpha+ {\m} \beta+ {\n}=0( {\p} \neq 0, {\m} \neq 0), then which one of the following is True?

Correct Answer is : When p+mf′(α)≠0,px+my+n=0 intersects the curve y=f(x)

When p+m f^{'}(\alpha)=0, p x+m y+n=0 intersects the curve y=f(x)

{\px}+ {\my}+ {\n}=0 is always a tangent to the curve {\y}= {\f}( {\x})

When p+m f^{'}(\alpha) \neq 0, p x+m y+n=0 intersects the curve y=f(x)

p x+m y+n=0 is never a tangent to the curve y=f(x)

AP EAPCET 16th May 2023 Shift 2 Solved Paper

Section: Mathematics

Question : 65 of 160

Marks: +1, -0

f(x) is a continuous function on ℝ and y=f(x) is a curve. If (α,β) is a point such that β=f(α) and pα+mβ+n=0(p≠0,m≠0), then which one of the following is True?

When p+mf′(α)=0,px+my+n=0 intersects the curve y=f(x)
px+my+n=0 is always a tangent to the curve y=f(x)
When p+mf′(α)≠0,px+my+n=0 intersects the curve y=f(x)
px+my+n=0 is never a tangent to the curve y=f(x)

Validate

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