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?

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TopNewestThere 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 · 3 years, 9 months ago

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In this case, making it a problem about understanding quadratic polynomials resolves it without necessarily knowing calculus. – Calvin Lin Staff · 3 years, 9 months ago

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– Kathleen Kasper · 3 years, 9 months ago

Thank you Calvin!Log in to reply