Differentiation

Find values of m for which the line y =2m-x is a tangent to the curve x^2+y^2 -3xy+2=0 Could the Brilliant community help me? I know one method is through implicit differentiation, which I do not really understand and hopefully someone can teach me. Other than implicit differentiation, are there other methods to solve this question?

Easy Math Editor

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Comments

There is a way to do it without calculus. If you solve the system of equations using substitution, you will get a quadratic equation with variable x as well as some m's. If the line is tangent to the curve, there is only ONE point of intersection, i.e., one solution, meaning the discriminant of the quadratic equals zero.

KATHLEEN KASPER - 8 years ago

I like your interpretation. There are often many different approaches to the same problem, and your solution can change according to the perspective that you use to view it.

In this case, making it a problem about understanding quadratic polynomials resolves it without necessarily knowing calculus.

Calvin Lin Staff - 8 years ago

Thank you Calvin!

KATHLEEN KASPER - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$