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Solve Lesson 58 Page 90 SBT Math 10 – Kite>


Topic

In the coordinate plane Oxygengive points USA(1 ; 1) and straight line : 3x + 4y + 3 = 0. Write the equation of the circle (OLD), know (OLD) has a mind USA and straight line cut (OLD) at two points WOMEN, P satisfy the triangle MNP even.

Solution method – See details

Find the radius of the circle (OLD)

Step 1: Calculate the distance from M to

Step 2: ConsiderMNP Everyone knows the length of the altitude line from USAcalculate the lengths of the sides of the triangle as the radius of (OLD)

Step 3: Write a circle PT with center USA and the radius found in step 2

Detailed explanation

Call H is the projection of USA go straight

We have: \(MH = d(M,\Delta ) = \frac{{\left| {3 + 4 + 3} \right|}}{{\sqrt {{3^2} + {4^2} } }} = 2\)

According to the assumption,MNP evenly \( \Rightarrow \widehat {MNH} = {60^0}\)

Consider \(\Delta MNH\) square at H yes \(MN = \frac{{MH}}}{{\sin \widehat {MNH}}} = \frac{2}{{\sin {{60}^0}}} = \frac{{4\sqrt 3 }}{3}\)\( \Rightarrow R = \frac{{4\sqrt 3 }}{3}\)

So (OLD) has PT: \({(x – 1)^2} + {(y – 1)^2} = \frac{{16}}{3}\)



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