2 years ago

Find the gradients of lines a and b

Mathematics

1 answer:

Yanka [14]2 years ago

3 0

Answer:

a 2

b -1

Step-by-step explanation:

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The vertex is (2,-4) and it is a minimum

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Answer:

(2,-5) and (2,1).

Step-by-step explanation:

We need to find the find all the points having an x coordinate of 2 whose distance from the point (-2,-4) is 5.

A circle with center (-2,-4) and radius 5 represents all the points whose distance from the point (-2,-4) is 5.

Standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

where, (h,k) is center and r is the radius.

$(x-(-2))^2+(y-(-4))^2=(5)^2$

$(x+2)^2+(y+2)^2=25$

Now, put x=2.

$(2+2)^2+(y+2)^2=25$

$(4)^2+(y+2)^2=25$

$(y+2)^2=25-16$

$(y+2)^2=9$

Taking square root on both sides.

$y+2=\pm\sqrt{9}$

$y+2=\pm3$

$y+2=-3\text{ or }y+2=3$

$y=-5\text{ or }y=1$

So, the y-coordinates of the points are -5 and 1.

Therefore, the required points are (2,-5) and (2,1).

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