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ExtremeBDS [4]
3 years ago
8

prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x^2 + y^2 = 5, i ha

ve 3/5 marks and i tried with perpendicular gradient.

Mathematics
2 answers:
Brums [2.3K]3 years ago
8 0

Answer:

I dont even know

Step-by-step explanation:

too complicated

Kamila [148]3 years ago
5 0

Answer:

You have to use the discriminant b^2 -4ac =0 because lines that cut a circle only once are tangents.

Step-by-step explanation:

I think you can use the perpendicular gradient, but it'll be more tedious because then you'll have to prove that the line touching the circle is perpendicular to the line from the centre to the circle to the point of intersection. You'll have to form an equation using the coordinates of the centre of the circle and the point of intersection. You probably had a careless mistake/ calculation error in this process.

Instead, try

1. equating the line to the circle (which you did), then

2. let the coefficient of x^2 be a, the coefficient of x be b, and the constant terms be c.

3. simplify b^2-4ac

3. prove that b^2-4ac=0 because there is only one real and distinct root, hence there is only one point of intersection.

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masha68 [24]

Answer:

\theta=1.72  radians

Step-by-step explanation:

Arc length and radius is given. So, we need to know the arc length formula for a circle.

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The complete sentence for the <em>unit</em> circle is:

<em>When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.</em>

<h3>How to complete a sentence with concepts from trigonometry</h3>

In this problem we have sentence to be completed by direct observation to the variables seen in a unit circle, a form used to teach trigonometric functions in a <em>graphic</em> manner. Now we proceed to present the complete sentence below:

<em>When t = 0, AP = 0, so sin t will begin at a value of 0. As t increases from 0 to π/2, sin t increases. Eventually, when t = π/2, OP will be 0, so sin t = AP will be 1.</em>

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Answer:

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