The equation of the circle is x2 + y2-6x-8y = 0. If you make a chord with length of 8 through the coordinate origin, the linear equation of the chord is __ (the result is written as a general equation of a straight line)

X2 + y2-6x-8y = 0, that is, (x-3) 2 + (y-4) 2 = 25. If the slope exists, let the straight line be y = KX
∵ the circle radius is 5, and the distance from the circle center m (3, 4) to the straight line is 3, | d = |3k − 4|
k2+1=3，
∴9k2-24k+16=9（k2+1），∴k=7
24. The straight line is y = 7
24x；
When the slope does not exist, the straight line is x = 0. Verify that its chord length is 8, so x = 0 is also the straight line. Therefore, the straight line is x = 0 or 7x-24y = 0
So the answer is: x = 0 or 7x-24y = 0

If there are two parallel strings in circle O with a radius of 5cm, and the lengths are 8cm and 6cm respectively, the distance between the two strings is a complete process

There are two cases:
When two parallel strings are on the same side of the center of the circle,
Distance between these two strings = √ (5) ²- three ²)- √(5 ²- four ²)= 4-3=1cm
When two parallel strings are not on the same side of the center of the circle,
Distance between these two strings = √ (5) ²- three ²)+ √(5 ²- four ²)= 4+3=7cm

Given that the lengths of two parallel chords of a circle are 6 and 2 √ 6 respectively, and the distance between the two lines is 3, find the radius of the circle

When the center of the circle is on both sides of two strings, OM + on = root sign (R ^ 2-3 ^ 2) + root sign (R ^ 2-6) = 3, r = root sign 10
When the center of the circle is on the same side of the two strings, on-om = root sign (R ^ 2-6) - root sign (R ^ 2-9) = 3, no solution
So, r = root 10

If there are two parallel strings in a circle with a radius of 5 cm, one is 8 cm long and the other is 6 cm long, the distance between the two strings is______ Centimeter

As shown in the figure, CD = 8, ab = 6, OA = OC = 5, ab ‖ CD, of ⊥ AB, OE ⊥ CD. According to the vertical diameter theorem, point E is the midpoint of CD, CE = 4cm, point F is the midpoint of AB, AF = 3cm. According to the Pythagorean theorem, OE = oc2 − CE2 = 3cm, of = oa2 − af2 = 4cm, there are two cases: ① when chord AB and chord CD are on the same side of the circle center

In a circle with a radius of 5cm, the lengths of two parallel lines are 6cm and 8cm respectively. Find the distance between the two strings

Distance from circle center to "6cm" chord = (5 ^ 2-3 ^ 2) ^ (1 / 2) = 4cm
Distance from circle center to "8cm" chord = (5 ^ 2-4 ^ 2) ^ (1 / 2) = 3cm
So: the distance between two strings = 4 + 3 = 7cm
Or: distance between two strings = 4-3 = 1cm

Lead two strings perpendicular to each other through a point on the circle. If the distance from the center of the circle to the two strings is 2 and 3 respectively, the lengths of the two strings are ___

According to ab ⊥ BC, OM ⊥ AB, on ⊥ BC,
Then the quadrilateral monb is rectangular,
So on = BM,
According to OM ⊥ AB,
AB = 2on = 4,
Similarly, BC = 6
The two strings are 6 and 4, respectively

The equation of the circle is x2 + y2-6x-8y = 0. If you make a chord with length of 8 through the coordinate origin, the linear equation of the chord is __ (the result is written as a general equation of a straight line)