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the line l is a tangent to the circle x^2+y^2=26 at the point A
A is the point (1,5)
The line crosses the x axis at point P
Work out the area of triangle OAP.

Sagot :

sqdancefan

Answer:

  65 square units

Step-by-step explanation:

Assuming point O refers to the origin, the segment OA has slope ...

  m = Δy/Δx = 5/1 = 5

Then the slope of the perpendicular line AP will be the negative reciprocal of this, -1/5.

The x-intercept of the line through (1, 5) with slope -1/5 can be found by setting y=0 in the point-slope equation for that line:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  0 -5 = (-1/5)(x -1)

  25 = x -1 . . . . . . . multiply by -5

  x = 26 . . . . . . . add 1

This means ΔOAP has a base length (OP) of 26 units and an altitude of 5 units. Its area is given by the formula ...

  A = 1/2bh

  A = 1/2(26)(5) = 65 . . . . square units

Triangle OAP has an area of 65 square units.

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