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Question Number 58254 by pete last updated on 20/Apr/19

$$\mathrm{The}\mathrm{line}3\mathrm{x}-2\mathrm{y}-5=0\mathrm{is}\mathrm{parallel}\mathrm{to}\mathrm{a}\mathrm{diameter}$$$$\mathrm{of}\mathrm{a}\mathrm{circle}{\mathrm{x}}^2+{\mathrm{y}}^2-4\mathrm{x}+2\mathrm{y}-4=0.\mathrm{find}\mathrm{the}$$$$\mathrm{equation}\mathrm{of}\mathrm{the}\mathrm{diameter}.$$

Answered by tanmay last updated on 20/Apr/19

$$x^2+y^2-4x+2y-4=0$$$$x^2-4x+4+y^2+2y+1-5-4=0$$$${(x-2)}^2+{(y+1)}^2=3^2$$$$centreofcircle(2,-1)radius=3$$$$3x-2y-5=0$$$$2y=3x-5$$$$y=\frac{3}{2}x-\frac{5}{2}\to slopem=\frac{3}{2}$$$$eqndiameter$$$$(y+1)=\frac{3}{2}(x-2)$$$$2y+2=3x-6$$$$3x-2y-8=0$$

Commented by pete last updated on 20/Apr/19

$$\mathrm{Thanks}\mathrm{very}\mathrm{much}\mathrm{sir}$$

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