The equation of the circle is (x-7)^2 + (y-4)^2 = 16. This tells us that the center of the circle, C, is at the point (7,4) and the radius of the circle is the square root of 16, which is 4.

The point P is at (1,7). We can find the distance from P to C by using the distance formula: sqrt[(x2-x1)^2 + (y2-y1)^2]. Substituting the coordinates of P and C gives us sqrt[(7-1)^2 + (4-7)^2] = sqrt[36 + 9] = sqrt[45] = 6.71 (rounded to two decimal places).

The length of the tangent from a point to a circle is given by sqrt[(PC)^2 - (radius)^2]. Substituting the values we have gives us sqrt[(6.71)^2 - 4^2] = sqrt[44.98 - 16] = sqrt[28.98] = 5.38 (rounded to two decimal places).

Therefore, the length of the two tangents from P to the circle is 5.38 units.

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The equation of the circle is (x-7)^2 + (y-4)^2 = 16. This tells us that the center of the circle, C, is at the point (7,4) and the radius of the circle is the square root of 16, which is 4.

The point P is at (1,7). We can find the distance from P to C by using the distance formula: sqrt[(x2-x1)^2 + (y2-y1)^2]. Substituting the coordinates of P and C gives us sqrt[(7-1)^2 + (4-7)^2] = sqrt[36 + 9] = sqrt[45] = 6.71 (rounded to two decimal places).

The length of the tangent from a point to a circle is given by sqrt[(PC)^2 - (radius)^2]. Substituting the values we have gives us sqrt[(6.71)^2 - 4^2] = sqrt[44.98 - 16] = sqrt[28.98] = 5.38 (rounded to two decimal places).

Therefore, the length of the two tangents from P to the circle is 5.38 units.

Knowee AI · Accepted Answer

The equation of the circle is (x-7)^2 + (y-4)^2 = 16. This tells us that the center of the circle, C, is at the point (7,4) and the radius of the circle is the square root of 16, which is 4.

The point P is at (1,7). We can find the distance from P to C by using the distance formula: sqrt[(x2-x1)^2 + (y2-y1)^2]. Substituting the coordinates of P and C gives us sqrt[(7-1)^2 + (4-7)^2] = sqrt[36 + 9] = sqrt[45] = 6.71 (rounded to two decimal places).

The length of the tangent from a point to a circle is given by sqrt[(PC)^2 - (radius)^2]. Substituting the values we have gives us sqrt[(6.71)^2 - 4^2] = sqrt[44.98 - 16] = sqrt[28.98] = 5.38 (rounded to two decimal places).

Therefore, the length of the two tangents from P to the circle is 5.38 units.

A circle with centre C has equation given below. The point P(1, 7) lies outside the circle. Find the length of two tangents to the circle from P tex](x-7)^{2} + (y-4)^{2} = 16[/tex]

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