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A curve has the equation, 6x^2 +3xy−y^2 +6=0 and passes through the point A (-5, 10). Find the equation of the normal to the curve at A.

Use implicit differentiation on original equation-
12x + 3x(dy/dx) + 3y - 2y(dy/dx) = 0
dy/dx= -12x -3y/(3x-2y) at A, x= -5 and y= 10 therefore, dy/dx=-6/7

To find the normal of t...

Answered by Chantal G. • Maths tutor

5818 Views

A curve has the equation y = (x^2 - 5)e^(x^2). Find the x-coordinates of the stationary points of the curve.

This requires the chain rule and the product rule to be used to differentiate the function. The substitution u = x² can be used to make this easier. Using this, du/dx = 2x and y = (u-5)e^u<...

Answered by Oliver J. • Maths tutor

3636 Views

Solve x^2 +11x +30 = 0

This is what we call a quadratic equation. To solve, first we need to factorise this equation into two brackets. (x + _ )(x + _) =0To fill the brackets, we need to find 2 numbers that add to 11 and multip...

Answered by Holly R. • Maths tutor

3953 Views

Compare and Contrast Meiosis and Mitosis

Similarities:Types of cell division which take place in Eukaryotic cellsDifferences:Meiosis - Occur in sex cells to produce haploid daughter cells; non-iden...

Answered by Lydia A. • Biology tutor

3323 Views

Consider the view that “spiritual or otherwise, Donne’s poems are consistently grounded in the physical world of his time.” [40]

In ‘Hymn to God, My God in my Sickness’, the poet reflects on past experience to prepare for a metaphysical future beyond the grave. Whilst the speaker’s mediations on his identity through the extended me...

Answered by Amelie M. • English tutor

3155 Views